Lecture 06_Machine Learning for Algo Trading.ipynb

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    "## <center><font color=navy>Algorithmic Trading in Python</font></center>\n",
    "### <center>Machine Learning for Algo Trading</center>\n",
    "#### <center>Ali Habibnia</center>"
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    "<img src=\"images/Life is like ML.jpg\" width=\"600\" height=\"800\"/>"
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    "## Optimization is at the heart of almost all machine learning algorithms \n",
    "\n",
    "* #### Pillars of Machine Learning: Linear algebra, probability analysis, and neumerical optimization\n",
    "\n",
    "Machine Learning has been an interesting topic for a lot of people since the 60s. However many people are afraid to start learning ML, mostly because it requires some knowledge of linear algebra and calculus. The course as you know is on Machine Learning and in this notebook we are going to let you go of the fear and see how with little effort practical models can be made to solve some real-world applications.\n",
    "\n",
    "* #### Building accurate models is a complex and challenging task. \n",
    "\n",
    "\n",
    "<img src=\"images/model.png\" />\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Econometrics vs. Machine Learning\n",
    "\n",
    "#### Goal of econometrics\n",
    "\n",
    "* #### \"the goal of econometrics is to find $\\hat\\theta$ where here we mean $\\hat\\theta$ to be the causal impact of X on y\n",
    "\n",
    "* #### The primary statistical concern of econometrics is sampling error. In other words, the goal is to quantify the uncertainty around $\\hat\\theta$ due to randomness in the sampling of the population. \n",
    "\n",
    "* #### The goal is to make counterfactual predictions.\n",
    "\n",
    "        What would happen to Amazon's profits if it changed its website layout?\n",
    "\n",
    "We don't get to observe the world under these alternative policies, so we can't simply find the answers in the data. Knowing the counterfactual requires being able to measure a causal effect. Being able to measure a causal effect requires making assumptions. That's what economics is all about!\n",
    "\n",
    "\n",
    "#### Goal of machine learning\n",
    "\n",
    "* #### In contrast, the goal of machine learning is to come up with the best possible out-of-sample prediction. \n",
    "\n",
    "* #### We refer to this as the primary concern of machine learning being \"$\\hat y$\"\n",
    "\n",
    "* #### The goal is to make sure that the best prediction is had by tuning and validating many different kinds of models. This is what cross-validation is all about, and it is what machine learning practitioners obsess about."
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    "### Translate between Econometrics (statistics) and Machine Learning\n",
    "\n",
    "|Econometrics|Machine Learning|\n",
    "|-----|-----|\n",
    "|X: Explanatory Variables |X: Input Variables|\n",
    "|y: Dependent Variable|y: Out put Variable|\n",
    "|$\\beta_0$: Intercept/Constant|b: Bias |\n",
    "|$\\beta$: Coeficients|$w$: weights|\n",
    "|$f()$: Linear Model|$f()$: Algorithms|\n",
    "|We estimate $\\beta$|We learn/train/fit $w$|\n",
    "|in-sample & out-of-samle|train (+validation)& test|\n",
    "|Shrinkage|Regularization|"
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    "## Definition of Machine Learning"
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    "\n",
    "    Machine Learning is a field of computer science that gives computers the ability to learn without being explicitly programmed. (Wikipedia)\n",
    "\n",
    "Machine learning was born during the early development of artificial intelligence and pattern recognition. Like all the other technologies it grew into the industry with the help of the businesses. There is one widely used formal definition of machine learning algorithms:\n",
    "\n",
    "    “A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E.” — Tom. M. Mitchell\n",
    "\n",
    "The definition states that our program has to learn from our data and should improve its performance. As a classical example, if we want to predict the house prices, first we can feed our algorithm with the data like current prices according to the area of a house, # of bedrooms etc. From the data, the algorithm learns and improves its guesses by reducing the errors for predictions. We can measure the performance by running the algorithm using a new input data with known results and take a look at the error rate. Our aim in here will be reducing the error rate."
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   "source": [
    "## Types of Machine Learning Problems and Tasks"
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    "### Supervised Learning"
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    "This type of ML algorithms works with the teacher model. It means that we have a dataset with inputs and output values; that is labeled data. We define a method to get known outputs for the inputs we have. As we improve our method by using all input-output pairs (this is called training), we can predict output values for new input data. This is called supervised learning. We learn the model using the *training data* and we test the model with unseen *test data*. So, we work both with input and output data. An example of supervised learning is predicting house prices. Another is to tell what digit or animal or picture is in a picture.\n",
    "\n",
    "Examples:\n",
    "\n",
    "- Regression (y is Continuous, i.e. linear regression)\n",
    "- Classification ( y is binary or multiclass, i.e. logistic regression)"
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    "### Unsupervised Learning"
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    "Unsupervised learning algorithms are used when we have only input data and no corresponding output values. There are no correct answers, therefore no teacher. These algorithms will be able to find hidden structure or relationship between different inputs. One of the best use cases for unsupervised learning algorithms is clustering problems.\n",
    "\n",
    "Example:\n",
    "\n",
    "- Clustering (i.e. K-means)\n",
    "- Dimensionality reduction (i.e. PCA)"
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   "source": [
    "### Semi-Supervised Learning"
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    "These algorithms are used where there is a huge amount of input data but only small amount of output (labeled) data. These problems sit in the middle of supervised and unsupervised learning. Therefore, supervised and unsupervised learning techniques are used together. One of the best examples for this is identifying objects in photos. Some photos are labeled as apples or lions but most of them are not labeled."
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    "### Reinforcement Learning"
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    "Reinforcement Learning is influenced by behavioral psychology with a rewarding system. We can think this is like playing with a dog. We have a dog (terminologically called an *agent*) and we have a park (*environment*) where he can do whatever he wants. Whenever dog gets back to you with a stick, you *reward* him with a food. After a while, the dog will start to have better approaches to find other sticks around. So, he will learn from the reward system. This approach in dog’s head is called reinforcement learning. We have an agent, environment, and reward. The difference between supervised learning is in the output data. In reinforcement learning, when the dog is walking around, he doesn’t know he will get a reward or not. He may never get a reward at all. But whenever he finds, he has learned to win. So, output data may come sometime later. In supervised learning, we know the output beforehand and make predictions by looking to them."
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    "Though many phenomena in the world can be adequately modeled using linear regression or classification, most interesting phenomena are generally nonlinear in nature. In order to deal with nonlinear phenomena, there have been a diversity of nonlinear models developed. For example parametric models assume that data follow some parameteric class of nonlinear function (e.g. polynomial, power, or exponential). Another class of models, the ones that are the focus of this notebook, are artificial neural networks (ANNs). ANNs are nonlinear models motivated by the physiological architecture of the nervous system. They involve a cascade of simple nonlinear computations that when aggregated can implement robust and complex nonlinear functions. \n",
    "\n",
    "There is a fascinating history that goes back to the 1940s full of ups and downs, twists and turns, friends and rivals, and successes and failures. An idea that was once sort of an ugly duckling has blossomed to become the belle of the ball.\n",
    "\n",
    "<img src='images/nn_timeline.jpg' style='width: 110%'/>\n"
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    "Early work in machine learning was largely informed by the current working theories of the brain. The first guys on the scene were Walter Pitts and Warren McCulloch. They had developed a technique known as “thresholded logic unit” and was designed to mimic the way a neuron was thought to work (which will be a recurring theme). \n",
    "\n",
    "However, it isn’t until [Frank Rosenblatt](https://en.wikipedia.org/wiki/Frank_Rosenblatt)’s “[perceptron](https://en.wikipedia.org/wiki/Perceptron)” that we see the first real precursor to modern neural networks. For its day, this thing was pretty impressive. It came with a learning procedure that would provably converge to the correct solution and could recognize letters and numbers. Rosenblatt was so confident that the perceptron would lead to true AI, that in 1959 he remarked:\n",
    "\n",
    "\n",
    "Rosenblatt’s perceptron began to garner quite a bit of attention, and one person in particular began to take notice. [Marvin Minsky](https://en.wikipedia.org/wiki/Marvin_Minsky), who is often thought of as one of the father’s of AI, began to sense that something was off with Rosenblatt’s perceptron. Minsky is quoted saying:\n",
    "\n",
    "\n",
    "\n",
    "    However, I started to worry about what such a machine could not do. For example, it could tell ‘E’s from ‘F’s, and ‘5’s from ‘6’s—things like that. But when there were disturbing stimuli near these figures that weren’t correlated with them the recognition was destroyed.\n",
    "\n",
    "Along with Seymor Papert, Minksy wrote a book entitled Perceptrons that effectively killed the perceptron, ending embryonic idea of a neural net. They showed that the perceptron was incapable of learning the simple **exclusive-or (XOR) function**. Worse, they proved that it was theoretically impossible for it to learn such a function, no matter how long you let it train. Now this isn’t surprising to us, as the model implied by the perceptron is a linear one and the XOR function is nonlinear, but at the time this was enough to kill all research on neural nets and usher in the first AI winter."
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    "### Let's start again from LR\n",
    "\n",
    "In the machine learning problems, we would like to earn a function $ f $, which predicts the output $ y $ from the input $ X $.\n",
    "$$\\begin{equation} y = f(X) \\end{equation}$$\n",
    "The $ f $ is referred to as the regression or classification function, and this learning problem is also known as function approximation in the field of mathematics.\n",
    "\n",
    "The regression problem is basically a good way to predict a continuous output $ Y $. And it is OK to use a discrete $ Y $ for the regression problem.\n",
    "A discrete $ Y $ leads the problem to the classification. For example, \"whether $ Y $ is 0 or 1\"\n",
    "\n",
    "We compute $ \\hat{f}$ from the training data $(\\mathbf{X}, \\mathbf{y})$ with whatever method, and then bring the test data and test it (how good the $\\hat{f}$ is?). \n",
    "Since, of course, it is extremely difficult to do such task without a clue, we simplify the situation by enchanting $ f $ with a special property."
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    "#### In Linear Regression\n",
    "\n",
    "The most absurd assumption is that $ f $ is linear.\n",
    "With $ X \\in \\mathbb{R}^p$ and $y \\in \\mathbb{R} $, we can write the linear regression function as\n",
    "$$\\begin{align} y &= f(X) \\\\ &= \\beta_0 + \\beta_1 X_1 + \\cdots + \\beta_p X_p \\\\ &= \\beta^T X, \\end{align}$$\n",
    "where, for brevity, $ X $ and $ \\beta $ are $ (p+1) $-vector containing the intercept, respectively.\n",
    "\n",
    "Now estimating $ f $ comes equivalent with finding $ \\beta $. Exaggeratingly speaking, linear regression is that you see the point cloud and draw your proper straight line. The linear regression fit $ \\hat{f} $ can be computed by the least squares.\n",
    "\n",
    "Here goes the simplest example.\n",
    "$$\\begin{equation} Y = \\beta_0 + \\beta_1 X \\end{equation}$$"
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   "source": [
    "import numpy as np\n",
    "import csv\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y = 0.096807 + 0.009595X\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"The simplest example for 1D linear regression\"\"\"\n",
    "# Generate data (sine-like wave)\n",
    "sample_size = 500\n",
    "sample_x = np.arange(0, 100, 100/sample_size)\n",
    "sample_y_true = np.sin(sample_x/10)/2 + sample_x*.01\n",
    "sample_y = sample_y_true + np.random.randn(sample_size)/4\n",
    "\n",
    "# Plot the data\n",
    "fig0 = plt.figure(0)\n",
    "ax0 = fig0.add_subplot(1, 1, 1)\n",
    "ax0.plot(sample_x, sample_y, 'o')\n",
    "\n",
    "# Implementation for the 1D linear regression\n",
    "mat_1x = np.vstack((np.ones(sample_size), sample_x)).T\n",
    "hat_beta = np.linalg.solve((mat_1x.T @ mat_1x),\n",
    "                              (mat_1x.T @ sample_y))\n",
    "\n",
    "# Compute the fit\n",
    "hat_y = mat_1x @ hat_beta\n",
    "\n",
    "# Plot the fit\n",
    "ax0.plot(sample_x, hat_y, linewidth=5)\n",
    "ax0.set_title('Linear Regression in 1D')\n",
    "print('Y = {:5f} + {:5f}X'.format(*hat_beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above picture, the computed straight line looks either good or bad. \n",
    "\n",
    "1. Does the line explains the original data? Bad. We actually did wrong with picking the model, since we saw the curvy data but fit with the straight line. (High bias) \n",
    "2. How well does the line predict a new data? Good. (Low variance)\n",
    "\n",
    "The straight line is simple, and simple is good, because\n",
    "\n",
    "- it makes the computation easier,\n",
    "- it makes the interpretation easier, and\n",
    "- it works well with the scarce data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Polynomial Regression\n",
    "\n",
    "A reason why many textbooks primarily deal with the linear regression is that it allows us to fit in more complex way with the same method. The idea is simple. Assume we want to fit a quadratic curve instead of a straight line. Then we change the original linear model\n",
    "$$\\begin{equation} Y = \\beta_0 + \\beta_1 X \\end{equation}$$\n",
    "to the quadratic model by adding the quadratic term as\n",
    "$$\\begin{equation} Y = \\beta_0 + \\beta_1 X + \\beta_2 X^2. \\end{equation}$$\n",
    "To get the estimate of $ \\beta_0, \\beta_1, \\beta_2 $, the corresponding training data change in the same way\n",
    "$$\\begin{equation} \\mathbf{X} = \\begin{bmatrix} 1 & x_1 \\\\ 1 & x_2 \\\\ \\vdots & \\vdots \\\\ 1 & x_N \\end{bmatrix} \\quad\\Longrightarrow\\quad \\mathbf{X} = \\begin{bmatrix} 1 & x_1 & x_1^2 \\\\ 1 & x_2 & x_2^2 \\\\ \\vdots & \\vdots & \\vdots \\\\ 1 & x_N & x_N^2 \\end{bmatrix}, \\end{equation}$$\n",
    "and the final computation is done with the plain linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y = 0.400251 + -0.008684X + 0.000183X^2\n",
      "Y = 0.600479 + -0.032881X + 0.000790X^2 + -0.000004X^3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\"\"\"1D polynomial regression\"\"\"\n",
    "# Plot the data\n",
    "fig1 = plt.figure(1, figsize=(10, 5))\n",
    "ax11 = fig1.add_subplot(1, 2, 1)\n",
    "ax11.plot(sample_x, sample_y, 'o')\n",
    "ax12 = fig1.add_subplot(1, 2, 2)\n",
    "ax12.plot(sample_x, sample_y, 'o')\n",
    "\n",
    "# Implementation for the 1D polynomial regression (quadratic/cubic)\n",
    "mat_1x2 = np.vstack((np.ones(sample_size),\n",
    "                     sample_x, sample_x**2)).T\n",
    "hat_beta2 = np.linalg.solve((mat_1x2.T @ mat_1x2),\n",
    "                            (mat_1x2.T @ sample_y))\n",
    "mat_1x3 = np.hstack((mat_1x2,\n",
    "                     (sample_x**3).reshape(-1, 1)))\n",
    "hat_beta3 = np.linalg.solve((mat_1x3.T @ mat_1x3),\n",
    "                            (mat_1x3.T @ sample_y))\n",
    "\n",
    "# Compute the fits\n",
    "hat_y2 = mat_1x2 @ hat_beta2\n",
    "hat_y3 = mat_1x3 @ hat_beta3\n",
    "\n",
    "# Plot the fit\n",
    "ax11.plot(sample_x, hat_y2, linewidth=5)\n",
    "ax11.set_title('Polynomial Regression (Quadratic)')\n",
    "ax12.plot(sample_x, hat_y3, linewidth=5)\n",
    "ax12.set_title('Polynomial Regression (Cubic)')\n",
    "print('Y = {:5f} + {:5f}X + {:5f}X^2'.format(*hat_beta2))\n",
    "print('Y = {:5f} + {:5f}X + {:5f}X^2 + {:5f}X^3'.format(*hat_beta3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural Networks  (Moving Beyond Linearity)\n",
    "\n",
    "- The central idea is to extract linear combinations of the inputs as derived features, and then model the target as a nonlinear function of these features. We note that the name \"neural networks\" derives from the fact that they were first developed as models for the human brain. Each unit represents a neuron, and the connections represent synapses.\n",
    "\n",
    "<img src=\"images/intro_nn.png\"/>\n",
    "\n",
    "\n",
    "\n",
    "#### Single layer perceptron\n",
    "\n",
    "The term _neural networks_ has evolved to encompass a large class of models and learning methods. Here we describe the most widely used \"vanilla\" neural net, sometimes called the **single hidden layer back-propagation network, or single layer perceptron**. See [Neural Network Architectures](https://towardsdatascience.com/the-mostly-complete-chart-of-neural-networks-explained-3fb6f2367464)\n",
    "\n",
    "There has been a great deal of _hype_ surrounding neural networks, making them seem magical and mysterious. As we make clear in this section, they are just nonlinear statistical models.\n",
    "\n",
    "A neural network is a two-stage regression or classification model, typically represented by a _network diagram_ as in FIGURE 11.2. (from The Elements of Statistical Learning) This network applies both to regression or classification.\n",
    "\n",
    "<img src='images/11.2.png' style='width: 60%'/>\n",
    "\n",
    "\n",
    "\n",
    "* For regression, typically $K=1$ and there is only one output unit $Y_1$ at the top.  \n",
    "  However, these networks can handle multiple quantitative responses in a seamless fashion, so we will deal with the general case.\n",
    "* For $K$-class classification, there are $K$ units at the top, with the $k$th unit modeling the probability of class $k$. There are $K$ target measurements $Y_k$ each being coded as a 0-1 variable for the $k$th class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $Z$\n",
    "\n",
    "Derived features $Z_m$ are created from linear combinations of the inputs, and the target $Y_k$ is modeled as a function of linear combinations of the $Z_m$,\n",
    "\n",
    "\\begin{align}\n",
    "Z_m &= \\sigma(\\alpha_{0m} + \\alpha_m^T X), & m=1,\\cdots,M, \\\\\n",
    "T_k &= \\beta_{0k} + \\beta_k^T Z, & k=1,\\cdots,K, \\\\\n",
    "f_k(X) &= g_k(T), & k=1,\\cdots,K.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sigmoid\n",
    "\n",
    "The activation function $\\sigma(v)$ is usually chosen to be the _sigmoid_\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma(v) = \\frac{1}{1+e^{-v}}.\n",
    "\\end{equation}\n",
    "\n",
    "See FIGURE 11.3 for a plot of the sigmoid function.\n",
    "\n",
    "<img src='images/11.3.png' style='width: 70%'/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"FIGURE 11.3. Plot of the sigmoid function.\n",
    "The scale parameter s controls the activation rate,\n",
    "and we can see that large s amounts to a hard activation at v=0.\n",
    "Note that sigmoid(s(v-v0)) shifts the activation threshold from 0 to v0.\"\"\"\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x: np.ndarray, s: float) -> np.ndarray:\n",
    "    return 1 / (1 + np.exp(-s * x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def sigmoid(x: np.ndarray, s: float) -> np.ndarray:\n",
    "    return 1 / (1 + np.exp(-s * x))\n",
    "\n",
    "x = np.linspace(-10, 10, 200)\n",
    "y_1 = sigmoid(x, 1)\n",
    "y_half = sigmoid(x, 0.5)\n",
    "y_10 = sigmoid(x, 10)\n",
    "\n",
    "fig = plt.figure(0, figsize=(10, 5))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(x, y_1, color='C3')\n",
    "ax.plot(x, y_half, '--', color='C0')\n",
    "ax.plot(x, y_10, '--', color='C4')\n",
    "ax.set_xlabel('v')\n",
    "ax.set_ylabel('sigmoid')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting Neural Networks\n",
    "\n",
    "The neural network model has unknown parameters, often called _weights_, and we seek values for them that make the model fit the training data well.\n",
    "\n",
    "We denote the complete set of weights by $\\theta$, which consists of\n",
    "\n",
    "\\begin{align}\n",
    "\\{ \\alpha_{0m}, \\alpha_m : m=1,2,\\cdots,M \\} & & M(p+1) \\text{ weights}, \\\\\n",
    "\\{ \\beta_{0k}, \\beta_k : k=1,2,\\cdots,K \\} & & K(M+1) \\text{ weights}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For regression, we use sum-of-squared errors as our measure of fit (error function)\n",
    "\n",
    "\\begin{equation}\n",
    "R(\\theta) = \\sum_{k=1}^K \\sum_{i=1}^N (y_{ik} - f_k(x_i))^2.\n",
    "\\end{equation}\n",
    "\n",
    "For classification we use either squared error or cross-entropy (deviance)\n",
    "\n",
    "\\begin{equation}\n",
    "R(\\theta) = -\\sum_{i=1}^N \\sum_{k=1}^K y_{ik}\\log f_k(x_i),\n",
    "\\end{equation}\n",
    "\n",
    "and the corresponding classifier is\n",
    "\n",
    "\\begin{equation}\n",
    "G(x) = \\arg\\max_k f_k(x).\n",
    "\\end{equation}\n",
    "\n",
    "With the softmax activation function and the cross-entropy error function, the neural network model is exactly a linear logistic regression in the hidden units, and all the parameters are estimated by maximum likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Back-propagation = gradient descent\n",
    "\n",
    "The generic approach to minimizing $R(\\theta)$ is by gradient descent, called _back-propagation_ in this setting. Because of the compositional form of the model, the gradient can be easily derived using the chain rule for differentiation.\n",
    "\n",
    "This can be computed by a forward and backward sweep over the network, keeping track only of quantities local to each unit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Back-propagation for squared error loss\n",
    "\n",
    "Let\n",
    "* $z_{mi} = \\sigma(\\alpha_{0m} + \\alpha_m^T x_i)$, and\n",
    "* $z_i = (z_{1i}, z_{2i}, \\cdots, z_{Mi})$.\n",
    "\n",
    "Then we have\n",
    "\n",
    "\\begin{align}\n",
    "R(\\theta) &\\equiv \\sum_{i=1}^N R_i \\\\\n",
    "&= \\sum_{i=1}^N \\sum_{k=1}^K \\left( y_{ik} - f_k(x_i) \\right)^2,\n",
    "\\end{align}\n",
    "\n",
    "with derivatives\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\partial R_i}{\\partial\\beta_{km}} &= -2\\left( y_{ik} - f_k(x_i) \\right) g_k'(\\beta_k^T z_i) z_{mi}, \\\\\n",
    "\\frac{\\partial R_i}{\\partial\\alpha_{ml}} &= -2\\sum_{k=1}^K \\left( y_{ik} - f_k(x_i) \\right) g_k'(\\beta_k^T z_i) \\beta_{km} \\sigma'(\\alpha_m^T x_i) x_{il}.\n",
    "\\end{align}\n",
    "\n",
    "Given these derivatives, a gradient descent update at the $(r+1)$st iteration has the form\n",
    "\n",
    "\\begin{align}\n",
    "\\beta_{km}^{(r+1)} &= \\beta_{km}^{(r)} - \\gamma_r \\sum_{i=1}^N \\frac{\\partial R_i}{\\partial\\beta_{km}^{(r)}}, \\\\\n",
    "\\alpha_{ml}^{(r+1)} &= \\alpha_{ml}^{(r)} - \\gamma_r \\sum_{i=1}^N \\frac{\\partial R_i}{\\partial \\alpha_{ml}^{(r)}},\n",
    "\\end{align}\n",
    "\n",
    "where $\\gamma_r$ is the learning rate, discussed below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Back-propagation equations\n",
    "\n",
    "Now write the gradients as\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\partial R_i}{\\partial\\beta_{km}} &= \\delta_{ki} z_{mi}, \\\\\n",
    "\\frac{\\partial R_i}{\\partial\\alpha_{ml}} &= s_{mi} x_{il}.\n",
    "\\end{align}\n",
    "\n",
    "The quantities $\\delta_{ki}$ and $s_{mi}$ are \"errors\" from the current model at the output and hidden layer units, respectively. From their definitions, these errors satisfy\n",
    "\n",
    "\\begin{equation}\n",
    "s_{mi} = \\sigma'(\\alpha_m^T x_i) \\sum_{k=1}^K \\beta_{km} \\delta_{ki},\n",
    "\\end{equation}\n",
    "\n",
    "known as the _back-propagation equations_. Using this, the gradient descent updates can be implemented with a two-pass algorithm.\n",
    "1. In the _forward pass_, the current weights are fixed and the predicted values $\\hat{f}_k(x_i)$ are computed from the formula  \n",
    "  \n",
    "  \\begin{align}\n",
    "  Z_m &= \\sigma(\\alpha_{0m} + \\alpha_m^T X), & m=1,\\cdots,M, \\\\\n",
    "  T_k &= \\beta_{0k} + \\beta_k^T Z, & k=1,\\cdots,K, \\\\\n",
    "  f_k(X) &= g_k(T), & k=1,\\cdots,K.\n",
    "  \\end{align}\n",
    "  \n",
    "2. In the _backward pass_, the errors $\\delta_{ki}$ are computed, and then back-propagated via  \n",
    "\n",
    "  \\begin{equation}\n",
    "  s_{mi} = \\sigma'(\\alpha_m^T x_i) \\sum_{k=1}^K \\beta_{km} \\delta_{ki},\n",
    "  \\end{equation}\n",
    "  \n",
    "  to give the errors $s_{mi}$.\n",
    "\n",
    "Both set of errors are then used to compute the gradients for the updates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advantages of back-propagation\n",
    "\n",
    "The advantages of back-propagation are its simple, local nature. In the back-propagation algorithm, each hidden unit passes and receives information only to and from units that share a connection. Hence it ca be implemented efficiently on a parallel architecture computer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network from Scratch in Python\n",
    "\n",
    "We will implement a simple 3-layer neural network from scratch. Implementing a network from scratch at least once is an extremely valuable exercise. It helps you gain an understanding of how neural networks work, and that is essential to designing effective models.\n",
    "\n",
    "\n",
    "<img src=\"images/nn.png\" style='width: 40%'/>\n",
    "\n",
    "<img src=\"images/bpro.png\" style='width: 40%'/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "— — — — — — — — — — — — — \n",
    "\n",
    "A typical training script has the following steps:\n",
    "\n",
    "- Define network\n",
    "- Initialize parameters\n",
    "- Loop over inputs\n",
    "- Forward input through network to get output\n",
    "- Compute loss with output and label\n",
    "- Backprop gradient\n",
    "- Update parameters with gradient descent.\n",
    "\n",
    "\n",
    "<img src='images/nn-3-layer-network.png' style='width: 55%'/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.97343103]\n",
      " [0.95288046]\n",
      " [0.05953422]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "#Input array\n",
    "X=np.array([[1,0,1,0],[1,0,1,1],[0,1,0,1]])\n",
    "\n",
    "#Output\n",
    "y=np.array([[1],[1],[0]])\n",
    "\n",
    "#Sigmoid Function\n",
    "def sigmoid (x):\n",
    "    return 1/(1 + np.exp(-x))\n",
    "\n",
    "#Derivative of Sigmoid Function\n",
    "def derivatives_sigmoid(x):\n",
    "    return x * (1 - x)\n",
    "\n",
    "#Variable initialization\n",
    "epoch=500 #Setting training iterations\n",
    "lr=0.5 #Setting learning rate\n",
    "inputlayer_neurons = X.shape[1] #number of features in data set\n",
    "hiddenlayer_neurons = 5 #number of hidden layers neurons\n",
    "output_neurons = 1 #number of neurons at output layer\n",
    "\n",
    "#weight and bias initialization\n",
    "wh=np.random.uniform(size=(inputlayer_neurons,hiddenlayer_neurons))\n",
    "bh=np.random.uniform(size=(1,hiddenlayer_neurons))\n",
    "wout=np.random.uniform(size=(hiddenlayer_neurons,output_neurons))\n",
    "bout=np.random.uniform(size=(1,output_neurons))\n",
    "\n",
    "for i in range(epoch):\n",
    "    #Forward Propogation\n",
    "    hidden_layer_input1=np.dot(X,wh)\n",
    "    hidden_layer_input=hidden_layer_input1 + bh\n",
    "    hiddenlayer_activations = sigmoid(hidden_layer_input)\n",
    "    output_layer_input1=np.dot(hiddenlayer_activations,wout)\n",
    "    output_layer_input= output_layer_input1+ bout\n",
    "    output = sigmoid(output_layer_input)\n",
    "\n",
    "    #Backpropagation\n",
    "    E = y-output\n",
    "    slope_output_layer = derivatives_sigmoid(output)\n",
    "    slope_hidden_layer = derivatives_sigmoid(hiddenlayer_activations)\n",
    "    d_output = E * slope_output_layer\n",
    "    Error_at_hidden_layer = d_output.dot(wout.T)\n",
    "    d_hiddenlayer = Error_at_hidden_layer * slope_hidden_layer\n",
    "    wout += hiddenlayer_activations.T.dot(d_output) *lr\n",
    "    bout += np.sum(d_output, axis=0,keepdims=True) *lr\n",
    "    wh += X.T.dot(d_hiddenlayer) *lr\n",
    "    bh += np.sum(d_hiddenlayer, axis=0,keepdims=True) *lr\n",
    "\n",
    "print (output)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.41151926,  1.69091766,  0.69541926,  0.08809065, -0.17885685],\n",
       "       [-1.14524741, -1.5788251 ,  1.14403567,  0.93863649,  0.47598779],\n",
       "       [ 1.2944632 ,  2.13861179,  0.31915562,  0.00545548, -0.26871841],\n",
       "       [-0.50986379, -0.80021544,  0.66635029,  0.51839964,  0.66993435]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Networks with Scikit-Learn\n",
    "\n",
    "https://scikit-learn.org/stable/modules/neural_networks_supervised.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-1.5, 1.5, 0.01).reshape(-1, 1)\n",
    "y = np.sin(2 * np.pi * x).ravel()\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.scatter(x, y, s=1, c='b', marker=\"s\", label='real')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn = MLPRegressor(\n",
    "    hidden_layer_sizes=(4,),  activation='tanh', solver='lbfgs', alpha=0.001, batch_size='auto',\n",
    "    learning_rate='constant', learning_rate_init=0.1, power_t=0.5, max_iter=5000, shuffle=True,\n",
    "    random_state=9, tol=0.0001, verbose=False, warm_start=False, momentum=0.9, nesterovs_momentum=True,\n",
    "    early_stopping=False, validation_fraction=0.1, beta_1=0.9, beta_2=0.999, epsilon=1e-08)\n",
    "\n",
    "n = nn.fit(x, y)\n",
    "test_x = np.arange(-1.5, 1.5, 0.05).reshape(-1, 1)\n",
    "test_y = nn.predict(test_x)\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.scatter(x, y, s=1, c='b', marker=\"s\", label='real')\n",
    "ax1.scatter(test_x,test_y, s=10, c='r', marker=\"o\", label='NN Prediction')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature extraction & Dimensionality Reduction with Deep Neural Nets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autoencoders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autoencoders are one of the unsupervised deep learning models. The aim of an autoencoder is dimensionality reduction and feature discovery. An autoencoder is trained to predict its own input, but to prevent the model from learning the identity mapping, some constraints are applied to the hidden units. \n",
    "\n",
    "“Autoencoding” is a data compression algorithm where the compression and decompression functions are 1) data-specific, 2) lossy, and 3) learned automatically from examples rather than engineered by a human. Additionally, in almost all contexts where the term “autoencoder” is used, the compression and decompression functions are implemented with neural networks.\n",
    "\n",
    "For building an autoencoder, three things are needed: an encoding function, a decoding function, and a distance function between the amount of information loss between the compressed representation of your data and the decompressed representation (i.e. a “loss” function).\n",
    "\n",
    "The simplest form of an autoencoder is a feedforward neural network where the input $x$ is fed to the hidden layer and the output of hidden layer is then fed to reconstruct the original inputs. A simple autoencoder is shown below:\n",
    "\n",
    "<center><img src=\"images/autoencoder.png\" width=\"650\" alt=\"A simple Autoencoder.\"></center>\n",
    "<center><img src=\"images/autoencoder2.png\" width=\"850\" alt=\"A simple Autoencoder.\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autoencoders map the data they are fed to a lower dimensional space by combining the data’s most important features. It encodes the original data into a more compact representation. It also decides how the data is combined, hence the auto in Autoencoder. We refer to these encoded features as latent variables.\n",
    "\n",
    "There are a few reasons doing this may be useful:\n",
    "\n",
    "1. Dimensionality reduction can decrease training time.\n",
    "1. Using latent feature representations may enhance model performance.\n",
    "\n",
    "\n",
    "Like the Autoencoder model, Principal Components Analysis (PCA) is also widely used as a dimensionality reduction technique. However, PCA maps the input in a different way than an Autoencoder.\n",
    "\n",
    "Both PCA and Autoencoder can be thought of as a lossy data compression algorithm. The quality of the data is not perfectly retained -- some of the original data get lost. Notice that it is different with feature selection. Feature selection algorithms discard some features of the data and retain salient features. The features they retain are typically chosen for statistical reasons, such as the correlation between the attribute and the target label. Autoencoder, as a feature extraction algorithm, projects data into a new space.\n",
    "\n",
    "Let's recap how PCA worked first."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA works by projecting input data onto the eigenvectors of the data’s covariance matrix. The covariance matrix quantifies the variance of the data and how much each variable varies with respect to one another. Eigenvectors are simply vectors that retain their span through a linear transformation, that is, they point in the same direction before and after the transformation. The covariance matrix transforms the original basis vectors to be oriented in the direction of the covariance between each variable. In simpler terms, the eigenvector allows us to re-frame the orientation of the original data to view it at a different angle without actually transforming the data. We are essentially extracting the component of each variable that leads to the most variance when we project the data onto these vectors. We can then select the dominant axes using the eigenvalues of the covariance matrix because they reflect the magnitude of the variance in the direction of their corresponding eigenvector.\n",
    "\n",
    "<center><img src=\"https://drive.google.com/uc?export=view&id=1ifTzuIC47I1DTP88cwUvtRQtG-_5OQIy\" width=\"450\" alt=\"A simple Autoencoder.\"></center>\n",
    "\n",
    "These projections result in a new space, where each basis vector encapsulates the most variance (i.e. the projections onto the eigenvector with the largest eigenvalue have the most variance, the ones on the second eigenvector have the second most variance, etc.). These new basis vectors are referred to as the principal components. We want principal components to be oriented in the direction of maximum variance because greater variance in attribute values can lead to better forecasting abilities. For example, say you’re trying to predict the price of a car given two attributes: color and brand. Suppose all the cars have the same color, but there are many brands among them. Guessing a car’s price based on its color — a feature with zero variance — would be pretty much impossible in this example. However, if we considered a feature with more variance, the brand, we will be able to come up with better price estimates because Audis and Ferraris tend to be priced higher than Hondas and Toyotas. The principal components resulting from PCA are linear combinations of the input variables . The linear nature of these principal components also allow us to interpret the transformed data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**PCA Pros**:\n",
    "\n",
    "* Reduces dimensionality\n",
    "* Interpretable\n",
    "* Fast run time\n",
    "\n",
    "**PCA Cons**:\n",
    "* Incapable of learning non-linear feature representations\n",
    "\n",
    "**Autoencoder Pros**:\n",
    "\n",
    "* Able to learn non-linear feature representations\n",
    "* Reduce dimensionality\n",
    "\n",
    "**Autoencoder Cons**:\n",
    "\n",
    "* Computationally expensive to train\n",
    "* Extremely uninterpretable\n",
    "* The underlying math is more complicated\n",
    "* Prone to overfitting, though this can be mitigated via regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showcase 1 - Neural Nets for predicting the movement of the stock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import yfinance as yf\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-01-02</th>\n",
       "      <td>20.799999</td>\n",
       "      <td>21.474001</td>\n",
       "      <td>20.733334</td>\n",
       "      <td>21.368668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-03</th>\n",
       "      <td>21.400000</td>\n",
       "      <td>21.683332</td>\n",
       "      <td>21.036667</td>\n",
       "      <td>21.150000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-04</th>\n",
       "      <td>20.858000</td>\n",
       "      <td>21.236668</td>\n",
       "      <td>20.378668</td>\n",
       "      <td>20.974667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-05</th>\n",
       "      <td>21.108000</td>\n",
       "      <td>21.149332</td>\n",
       "      <td>20.799999</td>\n",
       "      <td>21.105333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-01-08</th>\n",
       "      <td>21.066668</td>\n",
       "      <td>22.468000</td>\n",
       "      <td>21.033333</td>\n",
       "      <td>22.427334</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close\n",
       "Date                                                  \n",
       "2018-01-02  20.799999  21.474001  20.733334  21.368668\n",
       "2018-01-03  21.400000  21.683332  21.036667  21.150000\n",
       "2018-01-04  20.858000  21.236668  20.378668  20.974667\n",
       "2018-01-05  21.108000  21.149332  20.799999  21.105333\n",
       "2018-01-08  21.066668  22.468000  21.033333  22.427334"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# Download the data from Yahoo Finance\n",
    "df = yf.download('TSLA', start='2018-01-01', end='2023-01-01')\n",
    "\n",
    "df = df.dropna()\n",
    "df = df[['Open', 'High', 'Low', 'Close']]\n",
    "df.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then prepare the various input features which will be used by the artificial neural network learning for making the predictions. We define the following input features:\n",
    "\n",
    "- High minus Low price\n",
    "- Close minus Open price\n",
    "- Three day moving average\n",
    "- Ten day moving average\n",
    "- 30 day moving average\n",
    "- Standard deviation for a period of 5 days\n",
    "- Relative Strength Index\n",
    "- Williams %R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>O-C</th>\n",
       "      <th>H-L</th>\n",
       "      <th>3day MA</th>\n",
       "      <th>10day MA</th>\n",
       "      <th>30day MA</th>\n",
       "      <th>Std_dev</th>\n",
       "      <th>RSI</th>\n",
       "      <th>Williams %R</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-02-14</th>\n",
       "      <td>21.389334</td>\n",
       "      <td>21.744667</td>\n",
       "      <td>21.234667</td>\n",
       "      <td>21.487333</td>\n",
       "      <td>-0.098000</td>\n",
       "      <td>0.510000</td>\n",
       "      <td>21.106890</td>\n",
       "      <td>22.163000</td>\n",
       "      <td>22.400867</td>\n",
       "      <td>0.364370</td>\n",
       "      <td>42.108104</td>\n",
       "      <td>-48.848871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-15</th>\n",
       "      <td>21.633333</td>\n",
       "      <td>22.274668</td>\n",
       "      <td>21.493334</td>\n",
       "      <td>22.271334</td>\n",
       "      <td>-0.638000</td>\n",
       "      <td>0.781334</td>\n",
       "      <td>21.371112</td>\n",
       "      <td>21.949667</td>\n",
       "      <td>22.404822</td>\n",
       "      <td>0.595392</td>\n",
       "      <td>52.171565</td>\n",
       "      <td>-27.014469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-16</th>\n",
       "      <td>22.166668</td>\n",
       "      <td>22.874666</td>\n",
       "      <td>22.109333</td>\n",
       "      <td>22.365999</td>\n",
       "      <td>-0.199331</td>\n",
       "      <td>0.765333</td>\n",
       "      <td>21.778667</td>\n",
       "      <td>21.848467</td>\n",
       "      <td>22.442200</td>\n",
       "      <td>0.557207</td>\n",
       "      <td>53.274902</td>\n",
       "      <td>-24.378035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-20</th>\n",
       "      <td>22.298000</td>\n",
       "      <td>22.722668</td>\n",
       "      <td>22.100000</td>\n",
       "      <td>22.318001</td>\n",
       "      <td>-0.020000</td>\n",
       "      <td>0.622667</td>\n",
       "      <td>22.041555</td>\n",
       "      <td>21.793400</td>\n",
       "      <td>22.488578</td>\n",
       "      <td>0.433040</td>\n",
       "      <td>52.582984</td>\n",
       "      <td>-17.266302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-21</th>\n",
       "      <td>22.402000</td>\n",
       "      <td>22.646000</td>\n",
       "      <td>22.211332</td>\n",
       "      <td>22.219999</td>\n",
       "      <td>0.182001</td>\n",
       "      <td>0.434668</td>\n",
       "      <td>22.318445</td>\n",
       "      <td>21.804334</td>\n",
       "      <td>22.529000</td>\n",
       "      <td>0.364727</td>\n",
       "      <td>51.059742</td>\n",
       "      <td>-26.634148</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close       O-C       H-L  \\\n",
       "Date                                                                         \n",
       "2018-02-14  21.389334  21.744667  21.234667  21.487333 -0.098000  0.510000   \n",
       "2018-02-15  21.633333  22.274668  21.493334  22.271334 -0.638000  0.781334   \n",
       "2018-02-16  22.166668  22.874666  22.109333  22.365999 -0.199331  0.765333   \n",
       "2018-02-20  22.298000  22.722668  22.100000  22.318001 -0.020000  0.622667   \n",
       "2018-02-21  22.402000  22.646000  22.211332  22.219999  0.182001  0.434668   \n",
       "\n",
       "              3day MA   10day MA   30day MA   Std_dev        RSI  Williams %R  \n",
       "Date                                                                           \n",
       "2018-02-14  21.106890  22.163000  22.400867  0.364370  42.108104   -48.848871  \n",
       "2018-02-15  21.371112  21.949667  22.404822  0.595392  52.171565   -27.014469  \n",
       "2018-02-16  21.778667  21.848467  22.442200  0.557207  53.274902   -24.378035  \n",
       "2018-02-20  22.041555  21.793400  22.488578  0.433040  52.582984   -17.266302  \n",
       "2018-02-21  22.318445  21.804334  22.529000  0.364727  51.059742   -26.634148  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas_ta as pta\n",
    "\n",
    "# Predictor variables\n",
    "df['O-C'] = df.Open - df.Close\n",
    "df['H-L'] = df.High - df.Low\n",
    "df['3day MA'] = df.Close.shift(1).rolling(window=3).mean()\n",
    "df['10day MA'] = df.Close.shift(1).rolling(window=10).mean()\n",
    "df['30day MA'] = df.Close.shift(1).rolling(window=30).mean()\n",
    "df['Std_dev'] = df.Close.rolling(5).std()\n",
    "\n",
    "# Using pandas-ta for RSI\n",
    "df['RSI'] = pta.rsi(df.Close, length=9)\n",
    "\n",
    "# Using pandas-ta for Williams %R\n",
    "df['Williams %R'] = pta.willr(df.High, df.Low, df.Close, length=7)\n",
    "\n",
    "df = df.dropna()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then define the output value as price rise, which is a binary variable storing 1 when the closing price of tomorrow is greater than the closing price of today."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>O-C</th>\n",
       "      <th>H-L</th>\n",
       "      <th>3day MA</th>\n",
       "      <th>10day MA</th>\n",
       "      <th>30day MA</th>\n",
       "      <th>Std_dev</th>\n",
       "      <th>RSI</th>\n",
       "      <th>Williams %R</th>\n",
       "      <th>Price_Rise</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2018-02-14</th>\n",
       "      <td>21.389334</td>\n",
       "      <td>21.744667</td>\n",
       "      <td>21.234667</td>\n",
       "      <td>21.487333</td>\n",
       "      <td>-0.098000</td>\n",
       "      <td>0.510000</td>\n",
       "      <td>21.106890</td>\n",
       "      <td>22.163000</td>\n",
       "      <td>22.400867</td>\n",
       "      <td>0.364370</td>\n",
       "      <td>42.108104</td>\n",
       "      <td>-48.848871</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-15</th>\n",
       "      <td>21.633333</td>\n",
       "      <td>22.274668</td>\n",
       "      <td>21.493334</td>\n",
       "      <td>22.271334</td>\n",
       "      <td>-0.638000</td>\n",
       "      <td>0.781334</td>\n",
       "      <td>21.371112</td>\n",
       "      <td>21.949667</td>\n",
       "      <td>22.404822</td>\n",
       "      <td>0.595392</td>\n",
       "      <td>52.171565</td>\n",
       "      <td>-27.014469</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-16</th>\n",
       "      <td>22.166668</td>\n",
       "      <td>22.874666</td>\n",
       "      <td>22.109333</td>\n",
       "      <td>22.365999</td>\n",
       "      <td>-0.199331</td>\n",
       "      <td>0.765333</td>\n",
       "      <td>21.778667</td>\n",
       "      <td>21.848467</td>\n",
       "      <td>22.442200</td>\n",
       "      <td>0.557207</td>\n",
       "      <td>53.274902</td>\n",
       "      <td>-24.378035</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-20</th>\n",
       "      <td>22.298000</td>\n",
       "      <td>22.722668</td>\n",
       "      <td>22.100000</td>\n",
       "      <td>22.318001</td>\n",
       "      <td>-0.020000</td>\n",
       "      <td>0.622667</td>\n",
       "      <td>22.041555</td>\n",
       "      <td>21.793400</td>\n",
       "      <td>22.488578</td>\n",
       "      <td>0.433040</td>\n",
       "      <td>52.582984</td>\n",
       "      <td>-17.266302</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-02-21</th>\n",
       "      <td>22.402000</td>\n",
       "      <td>22.646000</td>\n",
       "      <td>22.211332</td>\n",
       "      <td>22.219999</td>\n",
       "      <td>0.182001</td>\n",
       "      <td>0.434668</td>\n",
       "      <td>22.318445</td>\n",
       "      <td>21.804334</td>\n",
       "      <td>22.529000</td>\n",
       "      <td>0.364727</td>\n",
       "      <td>51.059742</td>\n",
       "      <td>-26.634148</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close       O-C       H-L  \\\n",
       "Date                                                                         \n",
       "2018-02-14  21.389334  21.744667  21.234667  21.487333 -0.098000  0.510000   \n",
       "2018-02-15  21.633333  22.274668  21.493334  22.271334 -0.638000  0.781334   \n",
       "2018-02-16  22.166668  22.874666  22.109333  22.365999 -0.199331  0.765333   \n",
       "2018-02-20  22.298000  22.722668  22.100000  22.318001 -0.020000  0.622667   \n",
       "2018-02-21  22.402000  22.646000  22.211332  22.219999  0.182001  0.434668   \n",
       "\n",
       "              3day MA   10day MA   30day MA   Std_dev        RSI  Williams %R  \\\n",
       "Date                                                                            \n",
       "2018-02-14  21.106890  22.163000  22.400867  0.364370  42.108104   -48.848871   \n",
       "2018-02-15  21.371112  21.949667  22.404822  0.595392  52.171565   -27.014469   \n",
       "2018-02-16  21.778667  21.848467  22.442200  0.557207  53.274902   -24.378035   \n",
       "2018-02-20  22.041555  21.793400  22.488578  0.433040  52.582984   -17.266302   \n",
       "2018-02-21  22.318445  21.804334  22.529000  0.364727  51.059742   -26.634148   \n",
       "\n",
       "            Price_Rise  \n",
       "Date                    \n",
       "2018-02-14           1  \n",
       "2018-02-15           1  \n",
       "2018-02-16           0  \n",
       "2018-02-20           0  \n",
       "2018-02-21           1  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Price_Rise'] = np.where(df.Close.shift(-1) > df.Close, 1, 0)\n",
    "df = df.dropna()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input and output data\n",
    "X = df.iloc[:, 4:-1]\n",
    "y = df.iloc[:, -1]\n",
    "\n",
    "split = int(len(df)*0.8)\n",
    "X_train, X_test, y_train, y_test = X[:split], X[split:], y[:split], y[split:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building the Artificial Neural Network\n",
    "\n",
    "import tensorflow\n",
    "\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense\n",
    "from tensorflow.keras.layers import Dropout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier = Sequential()\n",
    "classifier.add(Dense(units = 32, kernel_initializer = 'uniform', activation = 'relu', input_dim = X.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Units: This defines the number of nodes or neurons in that particular layer. We have set this value to 128, meaning there will be 128 neurons in our hidden layer.\n",
    "- Kernel_initializer: This defines the starting values for the weights of the different neurons in the hidden layer. We have defined this to be ‘uniform’, which means that the weights will be initialized with values from a uniform distribution.\n",
    "- Activation: This is the activation function for the neurons in the particular hidden layer. Here we define the function as the rectified Linear Unit function or ‘relu’.\n",
    "- Input_dim: This defines the number of inputs to the hidden layer, we have defined this value to be equal to the number of columns of our input feature dataframe. This argument will not be required in the subsequent layers, as the model will know how many outputs the previous layer produced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We add a second hidden layer\n",
    "classifier.add(Dense(units = 32, kernel_initializer = 'uniform', activation = 'relu'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we built the output layer\n",
    "classifier.add(Dense(units = 1, kernel_initializer = 'uniform', activation = 'sigmoid'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The activation function is chosen to be the Sigmoid function because we would want the prediction to be a probability of market moving upwards."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier.compile(optimizer = 'adam', loss = 'binary_crossentropy', metrics = ['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Optimizer: The optimizer is chosen to be ‘adam’, which is an extension of the stochastic gradient descent.\n",
    "- Loss: This defines the loss to be optimized during the training period. We define this loss to be the mean squared error.\n",
    "- Metrics: This defines the list of metrics to be evaluated by the model during the testing and training phase. We have chosen accuracy as our evaluation metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "197/197 [==============================] - 2s 5ms/step - loss: 0.6930 - accuracy: 0.5005\n",
      "Epoch 2/10\n",
      "197/197 [==============================] - 1s 5ms/step - loss: 0.6922 - accuracy: 0.5259\n",
      "Epoch 3/10\n",
      "197/197 [==============================] - 1s 5ms/step - loss: 0.6917 - accuracy: 0.5259\n",
      "Epoch 4/10\n",
      "197/197 [==============================] - 1s 5ms/step - loss: 0.6912 - accuracy: 0.5259\n",
      "Epoch 5/10\n",
      "197/197 [==============================] - 1s 6ms/step - loss: 0.6904 - accuracy: 0.5046\n",
      "Epoch 6/10\n",
      "197/197 [==============================] - 1s 6ms/step - loss: 0.6899 - accuracy: 0.5351\n",
      "Epoch 7/10\n",
      "197/197 [==============================] - 1s 6ms/step - loss: 0.6890 - accuracy: 0.5229\n",
      "Epoch 8/10\n",
      "197/197 [==============================] - 1s 5ms/step - loss: 0.6894 - accuracy: 0.5361\n",
      "Epoch 9/10\n",
      "197/197 [==============================] - 1s 6ms/step - loss: 0.6892 - accuracy: 0.5361\n",
      "Epoch 10/10\n",
      "197/197 [==============================] - 1s 6ms/step - loss: 0.6886 - accuracy: 0.5371\n"
     ]
    }
   ],
   "source": [
    "model = classifier.fit(X_train, y_train, batch_size = 5, epochs = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8/8 [==============================] - 0s 4ms/step\n"
     ]
    }
   ],
   "source": [
    "y_pred = classifier.predict(X_test)\n",
    "y_pred = (y_pred > 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then convert y_pred to store binary values by storing the condition y_pred > 5. Now, the variable y_pred stores either True or False depending on whether the predicted value was greater or less than 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['y_pred'] = np.NaN\n",
    "df.iloc[(len(df) - len(y_pred)):,-1:] = y_pred.astype(np.float64)\n",
    "trade_df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Open</th>\n",
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       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th>2022-01-10</th>\n",
       "      <td>333.333344</td>\n",
       "      <td>353.033325</td>\n",
       "      <td>326.666656</td>\n",
       "      <td>352.706665</td>\n",
       "      <td>-19.373322</td>\n",
       "      <td>26.366669</td>\n",
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       "      <th>2022-01-12</th>\n",
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       "      <td>346.800110</td>\n",
       "      <td>9.412873</td>\n",
       "      <td>56.719871</td>\n",
       "      <td>-44.640350</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.069877</td>\n",
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       "    <tr>\n",
       "      <th>2022-01-13</th>\n",
       "      <td>369.690002</td>\n",
       "      <td>371.866669</td>\n",
       "      <td>342.179993</td>\n",
       "      <td>343.853333</td>\n",
       "      <td>25.836670</td>\n",
       "      <td>29.686676</td>\n",
       "      <td>358.748881</td>\n",
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       "      <td>339.959991</td>\n",
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       "      <td>337.793335</td>\n",
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      "text/plain": [
       "                  Open        High         Low       Close        O-C  \\\n",
       "Date                                                                    \n",
       "2022-01-10  333.333344  353.033325  326.666656  352.706665 -19.373322   \n",
       "2022-01-11  351.223328  358.616669  346.273346  354.799988  -3.576660   \n",
       "2022-01-12  359.616669  371.613342  357.529999  368.739990  -9.123322   \n",
       "2022-01-13  369.690002  371.866669  342.179993  343.853333  25.836670   \n",
       "2022-01-14  339.959991  350.666656  337.793335  349.869995  -9.910004   \n",
       "\n",
       "                  H-L     3day MA    10day MA    30day MA    Std_dev  \\\n",
       "Date                                                                   \n",
       "2022-01-10  26.366669  353.308889  364.162332  347.871111  15.278400   \n",
       "2022-01-11  12.343323  349.975555  362.968332  347.606666   7.314940   \n",
       "2022-01-12  14.083344  349.942220  362.165997  346.800110   9.412873   \n",
       "2022-01-13  29.686676  358.748881  362.833664  346.371887  10.576693   \n",
       "2022-01-14  12.873322  355.797770  361.540997  345.666998   9.214006   \n",
       "\n",
       "                  RSI  Williams %R  Price_Rise  y_pred  Tomorrows Returns  \n",
       "Date                                                                       \n",
       "2022-01-10  49.394709   -65.736831           1     0.0           0.005917  \n",
       "2022-01-11  50.383627   -62.982459           1     1.0           0.038538  \n",
       "2022-01-12  56.719871   -44.640350           0     1.0          -0.069877  \n",
       "2022-01-13  45.141677   -72.911625           1     1.0           0.017346  \n",
       "2022-01-14  48.027192   -48.665194           0     1.0          -0.018365  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trade_df = df.dropna().copy()  # Explicitly create a copy\n",
    "trade_df['Tomorrows Returns'] = 0.\n",
    "trade_df['Tomorrows Returns'] = np.log(trade_df['Close']/trade_df['Close'].shift(1))\n",
    "trade_df['Tomorrows Returns'] = trade_df['Tomorrows Returns'].shift(-1)\n",
    "trade_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
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       "      <td>-0.069877</td>\n",
       "      <td>-0.069877</td>\n",
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       "      <th>2022-01-13</th>\n",
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       "      <td>371.866669</td>\n",
       "      <td>342.179993</td>\n",
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       "                  Open        High         Low       Close        O-C  \\\n",
       "Date                                                                    \n",
       "2022-01-10  333.333344  353.033325  326.666656  352.706665 -19.373322   \n",
       "2022-01-11  351.223328  358.616669  346.273346  354.799988  -3.576660   \n",
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       "2022-01-14  339.959991  350.666656  337.793335  349.869995  -9.910004   \n",
       "\n",
       "                  H-L     3day MA    10day MA    30day MA    Std_dev  \\\n",
       "Date                                                                   \n",
       "2022-01-10  26.366669  353.308889  364.162332  347.871111  15.278400   \n",
       "2022-01-11  12.343323  349.975555  362.968332  347.606666   7.314940   \n",
       "2022-01-12  14.083344  349.942220  362.165997  346.800110   9.412873   \n",
       "2022-01-13  29.686676  358.748881  362.833664  346.371887  10.576693   \n",
       "2022-01-14  12.873322  355.797770  361.540997  345.666998   9.214006   \n",
       "\n",
       "                  RSI  Williams %R  Price_Rise  y_pred  Tomorrows Returns  \\\n",
       "Date                                                                        \n",
       "2022-01-10  49.394709   -65.736831           1     0.0           0.005917   \n",
       "2022-01-11  50.383627   -62.982459           1     1.0           0.038538   \n",
       "2022-01-12  56.719871   -44.640350           0     1.0          -0.069877   \n",
       "2022-01-13  45.141677   -72.911625           1     1.0           0.017346   \n",
       "2022-01-14  48.027192   -48.665194           0     1.0          -0.018365   \n",
       "\n",
       "            Strategy Returns  \n",
       "Date                          \n",
       "2022-01-10         -0.005917  \n",
       "2022-01-11          0.038538  \n",
       "2022-01-12         -0.069877  \n",
       "2022-01-13          0.017346  \n",
       "2022-01-14         -0.018365  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trade_df['Strategy Returns'] = 0.\n",
    "trade_df['Strategy Returns'] = np.where(trade_df['y_pred'] == True, trade_df['Tomorrows Returns'], - trade_df['Tomorrows Returns'])\n",
    "trade_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2022-01-10</th>\n",
       "      <td>333.333344</td>\n",
       "      <td>353.033325</td>\n",
       "      <td>326.666656</td>\n",
       "      <td>352.706665</td>\n",
       "      <td>-19.373322</td>\n",
       "      <td>26.366669</td>\n",
       "      <td>353.308889</td>\n",
       "      <td>364.162332</td>\n",
       "      <td>347.871111</td>\n",
       "      <td>15.278400</td>\n",
       "      <td>49.394709</td>\n",
       "      <td>-65.736831</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.005917</td>\n",
       "      <td>-0.005917</td>\n",
       "      <td>0.005917</td>\n",
       "      <td>-0.005917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-11</th>\n",
       "      <td>351.223328</td>\n",
       "      <td>358.616669</td>\n",
       "      <td>346.273346</td>\n",
       "      <td>354.799988</td>\n",
       "      <td>-3.576660</td>\n",
       "      <td>12.343323</td>\n",
       "      <td>349.975555</td>\n",
       "      <td>362.968332</td>\n",
       "      <td>347.606666</td>\n",
       "      <td>7.314940</td>\n",
       "      <td>50.383627</td>\n",
       "      <td>-62.982459</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.038538</td>\n",
       "      <td>0.038538</td>\n",
       "      <td>0.044455</td>\n",
       "      <td>0.032620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-12</th>\n",
       "      <td>359.616669</td>\n",
       "      <td>371.613342</td>\n",
       "      <td>357.529999</td>\n",
       "      <td>368.739990</td>\n",
       "      <td>-9.123322</td>\n",
       "      <td>14.083344</td>\n",
       "      <td>349.942220</td>\n",
       "      <td>362.165997</td>\n",
       "      <td>346.800110</td>\n",
       "      <td>9.412873</td>\n",
       "      <td>56.719871</td>\n",
       "      <td>-44.640350</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.069877</td>\n",
       "      <td>-0.069877</td>\n",
       "      <td>-0.025422</td>\n",
       "      <td>-0.037256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-13</th>\n",
       "      <td>369.690002</td>\n",
       "      <td>371.866669</td>\n",
       "      <td>342.179993</td>\n",
       "      <td>343.853333</td>\n",
       "      <td>25.836670</td>\n",
       "      <td>29.686676</td>\n",
       "      <td>358.748881</td>\n",
       "      <td>362.833664</td>\n",
       "      <td>346.371887</td>\n",
       "      <td>10.576693</td>\n",
       "      <td>45.141677</td>\n",
       "      <td>-72.911625</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.017346</td>\n",
       "      <td>0.017346</td>\n",
       "      <td>-0.008075</td>\n",
       "      <td>-0.019910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-14</th>\n",
       "      <td>339.959991</td>\n",
       "      <td>350.666656</td>\n",
       "      <td>337.793335</td>\n",
       "      <td>349.869995</td>\n",
       "      <td>-9.910004</td>\n",
       "      <td>12.873322</td>\n",
       "      <td>355.797770</td>\n",
       "      <td>361.540997</td>\n",
       "      <td>345.666998</td>\n",
       "      <td>9.214006</td>\n",
       "      <td>48.027192</td>\n",
       "      <td>-48.665194</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.018365</td>\n",
       "      <td>-0.018365</td>\n",
       "      <td>-0.026440</td>\n",
       "      <td>-0.038275</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Open        High         Low       Close        O-C  \\\n",
       "Date                                                                    \n",
       "2022-01-10  333.333344  353.033325  326.666656  352.706665 -19.373322   \n",
       "2022-01-11  351.223328  358.616669  346.273346  354.799988  -3.576660   \n",
       "2022-01-12  359.616669  371.613342  357.529999  368.739990  -9.123322   \n",
       "2022-01-13  369.690002  371.866669  342.179993  343.853333  25.836670   \n",
       "2022-01-14  339.959991  350.666656  337.793335  349.869995  -9.910004   \n",
       "\n",
       "                  H-L     3day MA    10day MA    30day MA    Std_dev  \\\n",
       "Date                                                                   \n",
       "2022-01-10  26.366669  353.308889  364.162332  347.871111  15.278400   \n",
       "2022-01-11  12.343323  349.975555  362.968332  347.606666   7.314940   \n",
       "2022-01-12  14.083344  349.942220  362.165997  346.800110   9.412873   \n",
       "2022-01-13  29.686676  358.748881  362.833664  346.371887  10.576693   \n",
       "2022-01-14  12.873322  355.797770  361.540997  345.666998   9.214006   \n",
       "\n",
       "                  RSI  Williams %R  Price_Rise  y_pred  Tomorrows Returns  \\\n",
       "Date                                                                        \n",
       "2022-01-10  49.394709   -65.736831           1     0.0           0.005917   \n",
       "2022-01-11  50.383627   -62.982459           1     1.0           0.038538   \n",
       "2022-01-12  56.719871   -44.640350           0     1.0          -0.069877   \n",
       "2022-01-13  45.141677   -72.911625           1     1.0           0.017346   \n",
       "2022-01-14  48.027192   -48.665194           0     1.0          -0.018365   \n",
       "\n",
       "            Strategy Returns  Cumulative Market Returns  \\\n",
       "Date                                                      \n",
       "2022-01-10         -0.005917                   0.005917   \n",
       "2022-01-11          0.038538                   0.044455   \n",
       "2022-01-12         -0.069877                  -0.025422   \n",
       "2022-01-13          0.017346                  -0.008075   \n",
       "2022-01-14         -0.018365                  -0.026440   \n",
       "\n",
       "            Cumulative Strategy Returns  \n",
       "Date                                     \n",
       "2022-01-10                    -0.005917  \n",
       "2022-01-11                     0.032620  \n",
       "2022-01-12                    -0.037256  \n",
       "2022-01-13                    -0.019910  \n",
       "2022-01-14                    -0.038275  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trade_df.loc[:, 'Cumulative Market Returns'] = np.cumsum(trade_df['Tomorrows Returns'])\n",
    "trade_df.loc[:, 'Cumulative Strategy Returns'] = np.cumsum(trade_df['Strategy Returns'])\n",
    "trade_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y9a36OS6/HGxtoXlzXXNLiHrqs52fccfyO8jOyybQM5Bru1xr0fOWHVpGQloCvx7+lW/2fEO35t24K+wuZoTOwNneuYZbLSpSXg9UTTl06BA2NjYEBQUBEBERQZs2bQBwdXUlOTkZb2/vUs8zBSfe3t6kpKSwePFiJk6cWOx5AJ06dSI+Pp4tW7YwYMAAsrOzOXz4MMHBwbi6urJ161b69evH999/X+z8t912G1dffTVDhgyhWbNm5b6Gdu3a8dhjj/Hyyy/z9ttvM3v2bI4cOUJgYCCpqalERUXRsWPHUq+nRYsWHDhwgE6dOrF06VJcXV0rde9OnjxJQEAAt99+O5mZmezYsYP//Oc/lTpHSdXu2crPwZoD/AYcAH40DGOfUmqeUmp8/mELAS+l1BHgAaBUeYi6YqNs8PPtCMAnvWDKTfbkfvRhtZd4WXtsLQlpCYAEW9VS3Z4tgDffhO3b4Yor9MxE0zmFqEcMw2DexnkEegYCcOai5UuIbTq1iW4tuhH1QBQLxi3AzsaOu1fezdXfXU1WblZNNVnUYykpKUyfPp2uXbvSvXt39u/fz7PPPgvArFmzGD16dEFCeVEeHh7cfvvthISEMGrUKPr06VOwz5RgHhoaSm5uLosXL+bRRx+lR48ehIaGsnnzZgAWLlzI7bffTmhoKKmpqbi7uxeco3fv3ri5uXHLLbdY9DruvPNONm7cSGpqKp9//jk33ngj3bt3Z8CAARw8eNDs63nppZcYN24cAwcOxLcKH9Q3bNhAjx496NmzJz/88AP33ntvpc9RimEY9fard+/eRm348+gfBs9iOD6tDJ7FWBWIYWzZUq1zTv1pqmH7nK3BsxhfRHxhpZZegp5/3jDAMDIyqn+uf/7R5/rxx6qfIy9PfwlhZeHR4QbPYnwc/rFhP8/eeHTtoxY9Lzs322g6v6kxZ8Wcgm15eXnGJ+GfGDyLMWXRFCMhNaGmmi3KsH///rpuQp1JTk4u+P7FF1805s6dW/BzVFSUERQUZOTm5tZF06zK3L8xsN0wE89c2hXk8/l76ET8TFvdm7VggANMn67X3qui7dHbuaztZYD0bFVLTAw0awZFxtWrrFcvaNKk6kOJK1fqRbAXLKh+W4Qo4af9P2GrbJnQeQJ+rn5EJZdMfTVvZ8xOUrNTGdJmSME2pRS39rqV+cPn8+O+H2n3Vjv+OfNPTTVdiGJWrFhRrGzCU089BcCXX35Jv379mD9/PjY2l1b4cWm92jL4ufoB4O7ozt1hd/NLYC4x8cdh4kRdeqAKkjKTaO/RHhtlI8FWdZRX0LSy7O312orh4eb3v/GGLpJakmHAiy/CuHG6DIUk2Qsry8nLYfGBxVzW9jK8m3jj7+ZP1EXLgq1Np/SHhyGth5Ta98SQJ9h9124cbB14a+tbVm2zEGWZMmUKERER7N27lxUrVmCa7Paf//yH06dPM2nSpDpuYe2TYAtwtnems3dn5vSdw7397yXXyOWRJ/pgrF+vE+WrkL+VlJFEM+dmNHNqRmKa2YmXojw5ObB+PZw+bb1gC6BTJ4iMNL9v0SJYvlxXpDdJSYHJk+GJJ+DGG2HQoLKfL0Ql5ebl8s3ub+j6XlcOJx5mWrdpAHqGtIU9W3+d+osOzTrg62o+NyWkeQiTgyez7OAyUrJSrNZ2IYTlJNjKt/euvTx/+fN09OrIc8Oe4+vUzbz49DBYuBBee61S58rKzSI9Jx13R3c8nT05lyE9W5X26qswfDhs22bdYKtjR4iPL13eIztbL2YNYKpwfOwYDBwIS5bo34Gvv4Zu3XSwZRg66d5KZULEpSMrN4sTF07w3Z7vCPkghGlLp+Fs78ySyUuYEToDyA+2LkZZVMJhT9weevr2LPeYm7rdRHpOOssOLjO735RXUh/EJMdwKOEQ0cnRJGcmk2fk1XWTqqy+3FNhfZX9t613RU3rStGio08PfZpDiYd4cs+3BN3an0mPPgpBQTBhgkXnSsrQPSPuTvnBlgwjVk5ysg5uBgwAf3+YMsV6586fBk1kJBSZZcO+fWCqx7Jjh368Nn/a/apVcOWVhc+/cAH+/Rf699cFcOfNgzlzzK/NKEQJI78aycaTeig62CeYRZMWcV2X67BRhZ99A9wCSM1OJSkzCQ8njzLPlZGTwbHzx7gx5MZyrzmw1UBau7fm273fMrV7YW2jPCOPFze9yOe7Pic2JZY7et/Bs8OexcWhnCWwatCFjAt0ercTyVnFV3qY2HUiiyYtqpM2VZWTkxOJiYl4eXlRD1anE1ZkGAaJiYk4OTlZ/BwJtsxQSrFw/EJOXDjBf+x20OaKLvSdOlUnVvfqVeHzkzLzgy1Hd7yaeHE25WxNN7lxeestPTnhzTehb1/rnrujLvPB4cPFg61t2/Sjo6PO6XrvPfD21oFWhw6Fx5mCtc8+049dusDcuTqRf/58CbhEuQzDYHv0dsYGjWVuv7lc0f6KYkGWib+bXvEs6mKU2WArPTudlKwUYlNiyTPy6OLdpdzr2igbJnedzFtb3yIpIwl3J3cMw+Celffw/vb3GdFuBL19e/P6ltdpYt+EeZfPs8rrrazv9nxHclYyr1+p25Gclcy64+tYcmAJ59PP08y5/LpM9UlAQABnzpwhPj6+rpsiaoCTkxMBAQEWHy/BVhmc7JxYOmUp/T7px/gr4vn3tDutr7gCWrSABx+E224r87kle7YOxMsiyBbJzYUHHoC334bx460faIEOnJQqnXe1fbue9WgaNkxPhy++KB5oQWGw9f33+vhNm3Re34svwujRMHSo9dssGo241DjSstMY1WEUV3a4sszj/F3zg63kKIKbB5fa/+jvj/LzwZ95deSrAHT27lzhta/tci2vbXmNlZEruSHkBu7/7X7e3/4+Dw14iFdGvoJSilNJp1hzdE2NBFsxyTG0cGlhNrg0+WTnJ4S2DOW+/vcV9AYNbDWQ1UdWs+74OiZ2nWj1dtUUe3t72rVrV9fNEPWE5GyVo3nT5qy4aQXpeZlcfYcryZcPhLNn9R/jcph6tjycPPB08iQxXRLkLbJypQ607rpLBzM1wdER2rTRPVtFbdsGYWH6Kz0dXFygyFphBdq1AxsbnUQ/YICuTP/883qfafhRiDIcv3AcgHbNyv8jXLRny5y/T//N6Yun+X7f9ygUnbw7VXjt/gH9aenSkqUHl/LI2kd4a+tb3Nvv3oJAC2Bk+5Fsi97GhYwLlXhVFTtx4QTt3mrHsxueLbXvYMJBbll2C+O/G8+OmB3c1vO2YsNuff374u7ozuojq63aJiFqkwRbFejq05VFkxax7+JRJlyTzjM3tGTXuf3lPsf0RmUaRryYeZHs3OxaaG0Dt3KlXgj8jTfAuQaXGOnYsTDYunhR51zt3q170kzDxJMm6baU5OioF7MGPTMR9DJA3t4670uIchw/nx9seZQfbJnK0fwb9S+vbX6N9Oz0gn3ZudnsjdsLwLKDy2jj0YYm9k0qvLaNsuGaTteweP9iXtvyGrP7zOaNUW8UC2yuaH8FeUYeG05sqOxLK9frW14nMzeT/235HzHJMQXbd8TsIOT9EBbtW8S++H20cmvFTd2Kr/ZmZ2PHyA4jWX1ktSSciwZLgi0LXNnhSt676j3+PPEn81ocYH7b03rIqwwlhxEBq39SbHQMQ+dHXXGFdQqYlscUbL38su6peuYZPWx5770wZIj+uu++sp9vGko0BVsAwcESbIkKWdqz5WTnhHcTbz4M/5CH1z7M1CVTyc3T7zn74/cXLMFjYFSYr1XUlOApGBjM6jWLt8e8XSpxu19AP5raN2Xt0bWVeVnlSkhL4JMdnzCi3QiycrP478b/FuxbFbmKXCOXg3MOcnTuUU7df8psXtboDqOJSo5if3z5H3SFqK8k2LLQHWF3cPHxi1zp0JWj7nkQHV3mscUS5J29AGQosSIHDsDJkzBmTM1fKyhIz3h87DE9o3D7dj007OOj87A2boTu3ct+fqdOukBq0QR7U7Aln7xFOY6fP06Lpi0s6olq5dYKJzsn7ux9J0sPLuW+1fdhGAY7Y3WJknEdxwGW5WuZXN7ucg7POcwH4z4wmzvlYOvAsLbDWB65nMycTIvPW57PIz4nPSedt0a/xW09b2PBjgUcO38MgG3R2+jo1ZEAt/ITjQe3HgzolTmEaIgk2KqEJvZNCPTswLFmwNGjZR5n6tlyc3Qr6NmS8g8VWLVKP9ZGsHX99TBrFvz9N6xYoavKV8YTT8DatXrpH5PgYD0kGWVZIUpxaTp+4XiFvVom7499n40zNvLBuA94cMCDvLvtXV7b/BoRsRE0sW/CnD5zACrVswUQ5BVUbpL6nL5zOJV0ipf+eqlS5y3L5tObCfQMJLh5ME9f9jT2Nvb83/r/A3Sw1cevTwVngEDPQJzsnNgTt8cqbRKitkmwVUkdArpxwRnORe4q85ikzCRcHFywtbGVYMtSK1fqgMWUD1WT/P3ho4/0zMOq8PWFyy4rvi04f8aYDCWKchw7f6zCfC2T/gH96eOvA5FXRr7C5ODJPPL7I3y751u6t+jOyA4j+WjcR9zYrfwaW5U1OnA0N4bcyPxN89kVW/b7nKWKBlR+rn7c2+9evt3zLauPrCY6OdqiYMvWxpauPl0l2BINlgRbldShre4FOXay7DehCxkXCmrjeDXJH0aUJXvKlpysSyhcdVVdt6TqTMHW3r112w5Rb+Xk5XAq6ZTFwVZRNsqGLyZ8wdA2Q4lPi6dny57YKBtm9Z5VIwVI3xz9Jj5NfRj33Tiik8tOmSjLD3t/IGxBGHvO7uHMxTPFAqpHBj2Cu5M7/1n6H4CCgLIi3Zp3Y89ZCbZEwyTBViW199bJ0UfPHizzmKTMJNwd3QEKerYS0xM5nHiY97e9z3U/XMeDvz1Y841tKNat08vlNORgy9tbz0qUni1RhjMXz5Br5Fo8jFiSk50TP0/5meu6XMcNITdYuXXFmcreXMi4wLhvx1VqTcX1x9dz89KbCY8JZ+7quQCE+YUV7G/m3IxHBz1KfFo8tsqW0JahFp23W/NuxKTEyAdX0SBJsFVJ7Zu1B+BoyqkyjzFVaAadJG+rbHl83eN0ercTs1fO5rejv/Hm1jcLcrsueatWgatr8dl9DVFVZyT++iu0bavre4lGKzJRF9KtSs+WSTPnZvw0+SeGtqn54rmhLUP5YeIP7Dq7ixt/urFgNmR59sXt49ofriXQM5CeLXuy4cQGbJQNvXyLr7wxt99cfF186daim0WTBQC6tegGIEOJokGSYKuSmjo0pUWuM8dyE8o8pmjPllKKGaEzGBs0lvevep/IeyJZfuNy8oy8gvXRLmmGofO1Ro7UM/wasuBg2L+/8jMS163TMzElub5RW354OY62jvT1r4GVEWrIVUFX8e6Yd1l+eHnBbMiyxCTHcNW3V+Fs78yqqau4M+xOQNcqbOpQvGZdE/smrJ62mi8mfGFxW7o1zw+2ZChRNEASbFVBB4cWHG2SWboKeb6iPVsAn4z/hCVTlnBXn7sI9AxkQKsBONk5se74utpqcv21bx+cOVM7sxBrWnAwpKTAqbJ7Pc06mD8kLWuoNVp5Rh6LDyxmTNAYXB1d67o5lXJXn7sKZkP+b8v/AAiPDi82tJicmczYb8eSmJbIiptW0MajDZODJ+Ns50w//35mz9u9RXe6tyinxEoJLV1a4uXsVWHPVlp2msXnFKK2SLBVBR06hHHME3jJzNToEye4EHsCjzyHwm3z5uk1/1auhJQUnOycGNx6sARboO8JNI5gKyREP1Z2KPHQIf0YF2fd9oh6Y/PpzUQnRzO56+S6bkqVvDLyFSZ1ncTDax9m9NejCfs4jKf+eArQif+TF09m99ndLJq0qGDI0MPJg79m/sULI16wShuUUoQ0Dym3sGlEbAQeL3mw6eQmq1xTCGuRYKsK2vsGc9oNkr//oli9rX+j/mXHx/NIssnG/Xx+/o1h6LXz3ngDxo4FT0+47DJGpLZgb9xezqacLf9iFy/qRa+PHavBV1SHVq3SBUT9/eu6JdVXlfIPaWl6CBGkZ6sRW7RvEY62jgWFSBsaG2XD19d9zbiO4/jt6G94N/Hm18O/YhgGd6+4m9VHVvPB2A8YE1T8Q1Mv3140b9rcau3o5NWJgwllT0568583yc4rXM5IiPpCgq0qGBM4BkPBh31toH9/Tr43nymLJtPvk35cmfcFWXbgnmOrD05OhpwcHXCtXat7uM6c4cpXfgLgpwM/lX+xBx6AhQvhq69q+FXVgYsX4a+/GvYsxKKaNdM1uCoTbEVGFuZ4Sc9Wg2QYBsfPHy83gfzf6H8Z0GqAZUOIFy/C0qXlLglWyrFjum7cs8/WWO6fg60DSyYv4eDsgzw37DmOnT/Gxzs+5uMdH/PYoMe4vfft1b+IYej3vEmTYOZMvYTWk0/qvEZ0tfzE9EQS0krnzMalxvHd3u8AqlSuQoiaJMFWFfQL6MfI9iN5bbQbT41zpnPMU/y6ezHX2YSQ6JQHgHtm/ppj5/KLmfr763X/XnoJXn2Vnscz6OPWhTf/eZO8/ftg6FCIjS1+oUWLiPpxIUNugR07VpTdoB074MoroWtXvdRMQ/H77zoQbQxDiCaVnZF4sMindOnZapB+O/ob7d9uj/er3ny1y/yHopMXTlo2C3HVKggMhOuug99+s7wRP/0EW7bolIU2bfTz166FvDzLz2EBe1t7Onl3Ykyg/j87d9VcWrq05Jlhz1jnAv/8o0cB/v1Xt/+LL/R75k03QV5ewdJEhxIOlXrqW/+8RVZuFs52zkQly2STS903u7+h/yf9ycjJqOumABJsVdn/XfZ/xGWeY37b01zrPYhDS/z5Zt5e3PP/Xd0z8nsrTMGWp2fhk4cNQynFQxeDiTwXya9LX9ZFPT/8UO/PyoKHH8aYPJnbb3bnrzbwY9ZOvd2ce++F8HDyDh2ENWtq5gXXhO+/1/dlwIC6bon1mGYkWvpH7uBBUAr8/KRnq4E6ek6nEvi5+nHv6ntLlXTJzMkkJiWGth5tKz7ZI4+AQ36+p2l42RKbNukF1o8cgQcf1D9feaXuHaqB9TrbNWtHZ+/OZOZmcn//+3Gyc7LOiT/5BFxc9AeW06fhwgX4/HP9fyMigk7enQBKDSUu2reIF/56gandphLSPER6ti5xqyJXMf3n6WyN2srJC5X4f1SDJNiqosGtB/PZNZ/x98y/+fa+v2gVHonTi68y0VMvmOqemj8EkJhfgM/Lq/DJnp7QqxfX/RFLG/c2fHguP0BasEAnSw8ejPHaa7z4UD9WNU/CWTnwp3+OXjC5pIgIVsX+RZt7DRyfMvg5dkPNvWhriorSiz/PnNnwSz4UFRxcPA+rIgcPQrt20KqV9Gw1UKYhrc+v+ZzzGed54583iu0/ffE0AG3c25R/osOH9QoEDzwAtraWDwfm5enh+CFDoH17ePllPcP38cd1z9Djj+uiwVZ2fZfr8WniU1DioVw5OTBnDoSHm98fGQlbt+oPYFOm6IDL5Mor9eNvv9HGvQ2Oto7Fgq1NJzdx89KbGdRqEJ+M/wQ/Vz/p2bqEbYvaxsRFE3FzdAMgNiW2gmfUDgm2qmFG6AwGtspfX8/JCR56iNtufBWHXAhMzg8gzPVsAYwYgd2WrYxqM5wtjnEYfr4QEwMhISSePsQ1/wvjSZetTOo6ibk972C7H6RuWFuqDcZ77/LwKIWtqxsKxebMIzX4iq3oo4/0H4m77qrrlliXpUnyJ07o4ZJ166BzZ119Xnq2GqSEtAQ8nDzo49+HiV0n8vqW14u9wZ+4cAKANh4VBFs/5edvTpoELVtaHmzt2wfnz+tgy8TREebP1x9mXn4ZunQpnPVqJc8Oe5Yjc48U/FEr1+LF8N57cOedxXva0tLghht0r1z//vrn224r/twWLaBnT1i9GlsbW4K8gjiUqF/LgfgDXPP9NbT1aMuyG5bhZOeEv6u/9Gxdoo6cO8LYb8fSomkLFk1aBEiw1Wj1D+hPyjdt6Xwu/9aaerbMBFtkZ9PnZA5JjgZH594MPXrw5+gu9HigCb+l7eat0W/xw8QfGNblKnJsYcuu5cXPcf48f278in0+Bk8Pe4YOee4cNRJrZNjAqgwDPv5YJ8a3b1/XrbGurl31o7lgyzDgzTehVy/dm/XAAzqhfs4c8PGRnq0GKiE9Ae8m3gC8MPwFMnMzeWTtIwX7TcMYFfZsLV4M/frpXk5/f8uDrU35ZQ6KBlugh6c/+QR++UXng/7vf5adz0J2NnaWBVqGoQM+JyfdO79kSeG+H37QX488At9+q3vi+pmpyzV6NGzeDBcv0tm7MwcTDhKbEsuYb8bgYOvAqqmrCtah9XP141z6OdKzZUWGS8nZlLOM+noUBgarp60uWAZKgq1GzN7NA5Ly8zbK6tm6/HIICKDPez8DsK29I/97bxrD++yjiZMr/9z6D3P7zUUpxaBWg7AxFBszSnwy/ewz3uuRhae9OzeE3ECgkx9HXHMKr1lfnTih3/zHj6/rllifh4f+Q2luQerNm+H++/UQ0auv6vyaXbv0BAFTsFXfA2VRSkJaYbAV5BXEwwMf5qvdXxWsEHEy6SQ2yoYAtwDzJ/jnHxg1Sk90mZxfh8vfXw8FWuKvv3TOXzszCfhKwdVX64T5xYshM7OyL6/6fv8dIiLgrbf0h5Enn9TDigDbtoGbG7z4Itx4I/znP7rNJY0cqZ/z99908urE0fNHGfTpIBLSElh+0/Ji6036ufoBEJMSUwsvTtQHKVkpjP12LLEpsSy/cTkdvTrSzLkZ9jb2Emw1au7uOrETdODj4lKY9Gpibw/33kvXY8k4ZcPPOft4dN1jjOs4jvBZ4fT07VlwqKujK72UHxs9k3U3O0BeHmc+e4ulXeDWPrNwtnemQ7MOHPUEIzKydl5nVe3YoR979Sr/uIaqrBmJ27bpx19/hYcegg4dCvc1b67zapKSSj9P1GtFgy2AJ4Y8QWv31sxeOZvs3GxOJp3E39Ufe9siuYmGoX8frrpKTxDZsUP3/txzj94fEGB5z9auXRAWZj5IMbnpJj3UWJkZjtby88/6PXD6dPjvf/Vw5pdf6n3btkHv3mBTwZ+i0FD9uGcPA1sNJM/Io3nT5vx646/FFrkG8HfTNfuiLkre1qUgz8hj4o8TiYiN4MeJP9IvQPeM2igbWri0IDZVgq3Gy9298I9mYmLx5Piibr8d+6au9Exy5sfDS8gz8nhz1Jtma/GEundivw+6NwRg9Wo+8jlFno3irjCd9xQY0I1UBzh7eEcNvCgr2rED7OwKK643NsHBcOBA6TpJ27frHoiWLUs/x8dHP8pQYoNTMthqYt+Et0a/xd64vbz777ucvHCyeL7WTTfpD1t9++qk8BdfhOPH9VCaabKIv7+ut5WSQrlycnRyeZcu5R83YoT+Hfvmm9L7fvhB966GhuoZ0aZeJ2vZtk0Hg46OMGGCft3PPKPfI3ftgj59Kj5Hs2Y6AN2zhzGBY0h7Io0tt27h8naXlzrU1LMleVuXhv3x+/nt6G+8MOIFxnYcW2xfS5eW0rPVqHl4FB9GLDmEaOLuDp99RliXEYBe9LVod3hRQX4hxDeFpIMRAGS+9xYL+tgwLrDwOYGBOqI/cryMGT/1xY4dOiBxstJ08fomOBgyMvQf0KLCw/UfHXOa51fZliT5GpeYlsjKyJVWOZdhGDrYcvYutv2aTtcwJnAMz2x4hn3x+wrztQwDVqzQAcd77+nfkcceKz77DgpXVCird8sw9ASTo0d1j2hFwZa9PUycCMuXQ3qRXKb//U8nqEdG6g9Ad92lh/usJSursOcNdO/bSy/pIdI779RttyTYAujWDfbsQSmFs71zmYf5u+p7J8HWpeFcuk6b6e3bu9Q+CbYau6I9W+UFWwDXX8+AITcBMLvP7DIPCwzsC0DkkX/hyBF+Or2GuCZ5zOk/t/CYljo5+0hc2ctZVMqOHYUJ/tZiGDroaKxDiFA4I/GVV2DGDF3dOzlZD5/0Lv2GAEjPlgXSstMwrJDT9sH2Dxj77diC+ljVbVNGTkaxni3Q6/i9PeZtMnMzSUhLKAy2zp/XPVaTJsHdd+t8JXMqCraefVbP0DtwQP9cUbAFcO21Og1hbf6s5rff1sPZkybpEiTbtkGPHjoYtJY9e3TAVTSguvxynYP1/ff658oEWwcOVFjGwsPJAyc7Jyn/cIkw1bVzd3Ivta9l00YSbCmlPJVSa5VSkfmPzcwcE6qU2qKU2qeU2q2UmlKdazYI7u76DTUvr/xhxHyTgiexfvp6RgeOLvOYIP/uAETG7IUPPuDdvhDk3p4r2l9RcEwb9zbYGoojyVYo4hYbq6div2CdRWQLREfrgKIxB1umGYkff6xnVwUHwxNP6ECzrGBLerbKFZMcg9crXvRe0Ju1R0uXQKmMyHM6p3HVkVXVbpepxlbJYAsg0DOQRwc9ChQp+2Dq7TSXzF5URcHW2rWwe7de1gegU6eKGztsmO51X7oUPvhAF0O+9lo9tGhnp3udRo6Ev/8uzA2tLlNtwJIBlel9xccHWre27FzduunArYKcVKWUlH+4hCRl5gdbjmaCLZeWxKXGlbuUVm2pbs/WY8A6wzCCgHX5P5eUBvzHMIxgYDTwplLKo5rXrd/c3XWglZJScc8Wegr1sLa6qnxZOnjqZOrIxEjCV3zMllYwu/9cbFThP6G9rT1t8lw5mhkDqamWtzcpCU6dKr5t4UL9CdLcrLrqaOzJ8aB7K266Sc88PH5c/6F59129r6KeLSvXQmoswmPCycjJ4FTSKaYsnkJadtWDAVOPljWGEssLtgAeH/w4Tw99mgmdJ+gNlQ22Dh7UCeZF8/9yc/XQHOjeIT8//Z5TEXt7GDdOP+fuu/Usxe+/L15UeORIHdCYyklU17Zt+sNm27bFt4eFwdy5uue3vMT+orp104979lR4aBuPNvxz5h8p/3AJuJBxAdA9miW1dGlJnpFndi3N2lbdYOsa4Iv8778AJpQ8wDCMw4ZhROZ/Hw3EAT7VvG79Znrju3DBomDLEk3smxCQ04QjGdG81zmZpjZOTA+dXuq4QO+ORHrk6TXWLHX77Xo9tdBQvbba7t26mj1Y/4//jh36zbVHD+uet7755ht4/XX9R8aUoxMYaD45HnTy8MSJug5XQ1pyqZbsj98PwCfjP+F8xnm+3/t9lc919LwOttafWF+toA0qDrac7Z2Zd/k8mjfN77k8dkw/VhRsNW2qe6FefFH3Pj34YGFZkMjIwp6nrCzLhhBNrrtO5xOOGQOLFpWeJT14sN72+++Wn7M8puR4cwHVW2/poXZLde6sy6ZYEGw9MfgJjl84znN/PleJxoqGqNxhRBf9flsfhhKrG2y1MAzDVMwkFmhR3sFKqb6AA1BmsoRSapZSartSant8Q81f8fDQj6dP60+hFQwjWirIviXb/eC7boqpoTebjeR7dxlBREtIXGpm1lFZDh/WgYCLi84F6dED49QpbpnpyQqHk9YbUgAdbHXurP+YXCpcXXVPwdat5R/32Wd6yHHmzNppVwOyP34/vi6+XNPpGoJ9gnn333erlL+Vlp1GbEosQ9sMJSMngw0nNlSrXRUFW6UcP64/fJWVq1VUQH5driuv1IHJG/nLAO3cqR8H66XBKhVsTZigP4gtWaID/JKaNIFBg/QHhOouYn38uP7gdtll1TuPiaOjHi4tL9hKS4PHH2eEeyi397qdVze/yqmkU2UfLxq8pMwknOyccLB1KLWvQQVbSqnflVJ7zXxdU/Q4Q7/zlfnup5TyBb4CbjEMo8z/xYZhLDAMI8wwjDAfnwbaAWbq2TINGVihZwsgyKM9B3wgw87gzjDzy9xcFzyRXBv45dgq/QnWEtHRemr4X3/p7z/8kPVP3MDnrc/xfQgV5kjw6ae6MKMlduzQib2XGgeHin8PXFx0snJUVI2sZdeQ7Y/fT3DzYJRSzOk7h52xO/nnjIW/c0UcO697lm4JvQUbZcOW01uq1a4qBVsV9WqZPPecLkS6apX+vXjwQV2mISJCD/3dd58+rnNnyxuslK7GXt5M4Ftu0Ynopt7tqvryS329qVOrd56iKlp26LPP9GzHlSu5qdtN5Bl5VpkIIeqvCxkXzHY8QAMLtgzDuMIwjBAzX8uAs/lBlCmYMpvdq5RyA1YATxqGUfl3yIbGFGyZhgys1bPVbRgAYS16Fit6WlRv3960cWjOT+0zYcOGik+alaUT1v10bRpatoQ77uDDUJ0jcsgbnTdSlpwcnf/xxBMVXysuTk/5bsz5WtXlnf9H29qzQBswwzDYH7+frt564sG07tNwc3TjvW3vVfpcpj+8XX264uviW+0ZawlpCdgomzLf7EupTLB13XX6y8ZGBy6DB+sK64sW6Rp148bp2YQTJ1a5/WZNm6Y/fD3ySOlcTkvl5enJISNGWJ4Ab4nOnQvLXZi7pik3Mjoanyb6w3p8WgMdIREWScpMMpscD9DCRQ+21YfVBKo7jPgLYEocmg4sK3mAUsoBWAp8aRjG4mper2EoGWxZqWerk5+ekXhH37vLPEYpxfXBk1jTAZIiKhi2Aj3rEAqDLfSn/6UHl2JnY8dBbzDKC7YiI/USIJs2FVbNL4tp+EOCrbKZAvOEuk/orC9OXzxNanYqXX10sOXi4MKMHjP4cd+PnE05W6lzmXq22jdrj7+bP2cuWrgkThkS0hLwdPbE1sa24oPz8vRSVZYGW0U5OcGyZXot0ePHde+wo6Ne9qlFudkblaeUXige9JJaycmVP8eKFbqdM2ZYtWl06qQ/4B0101v1+++FHwyjowt6G+NTJdhqzJIykszma4F+r+jo1ZFPd35a55MlqhtsvQSMVEpFAlfk/4xSKkwp9Un+MZOBocAMpVRE/ldoNa9bv9XQMOLowNF8Ov5TpvconRhf1LWhN5BtqxOAKxSjI/6TXna8+c+bDP1sKIFvB2KjbJjdZzbJjhB7JKLs55vyJ3JyKl4KxDQTsRaHEQ8mHCQ7twENyUnPFqB7s+JS4wiPDmd7tC4fYAq2AO7uczfZedl8suOTsk5h1tHzR3FzdMPL2YsAt4Dq92ylJ1g+hBgTo3uSq7r4uqenHlLs3l3PJKxJHTroHrS9e/V6jZWpKr9vH9x8sx7yu+4667bLNGRa8gPg+fN6WLVlS31/o6IKFqauDzPRRM0pbxgR4IOxHxB5LpJnNjxTe40yo1rBlmEYiYZhjDAMIyh/uPFc/vbthmHclv/914Zh2BuGEVrkK8IKba+/TAny//yjE07btCn3cEvZ29pzS89biq+xZkbPlj1RBuy5YMFMwuhoHh8BbXffwv2/3c+FjAv832X/R8QdEYzrOA6Ag2fNrPNnsnu3niHk5aXX/CvPjh36jdB0f2rYzpiddH2vK1/u+rJWrmcVpmDrEuvZ+jfqXx5d+yjX/3g9oR+G4vaSGy1ea0HYx2FMWaxL8xUNtjp5d2Jk+5F8GP4hOXmWBwJHzx+lQ7MOBbWYqtOzlWfkcfz8ccuDLVNvTFV6tkzattVlHyZMqPo5LDVqlK7HtXq1XrPRkgkJ0dF6vUdnZx0YOpdd6b1KTPXEiuZtZWbqGZtHj8J33+l7FB2NnY0dns6eMozYyJU3jAgwvN1wZvWaxYLwBQXV5uuCXZ1duTFzctIJrFlZcP31OuCqRU0dmtLe8GCvEac/kdqV888cHc36dhDqFcKim5YS6BlYsMvFQS8hcuh8JJd36qTzRvr1K/78PXugY0ddS+rXX/XsS9syhlQiIgoXlK0F/9vyPwwMwmPCuZVba+261WIaRrzEerbuW30f26K30aFZBzp4duCyNpfRwbMDXs5evLL5FXLycgp6Kkxm95nNhB8m8MuhX7iui/kelKzcLPbG7SU8OpwdMTvYfHozI9uPBCDALYCLmRdJzkw2ux5pRR5d+yjhMeG8MeoNy57w22/6/0ZZtdbqo9tv10HMyy/r3q6HHir72ORknUeWmAgbN1rtQ2Yxbm7g61vYs5WXp4cq//wTvv1WF2799FN9ffTEBQm2GrcLGRfKDbYAXhn5Ck8MeQJPZ+uMMlWFBFs1QSk9lJiQYN2ZOJUQ0rQde7136jfK8qpLR0cT7QrD/XsVC7QA/N38aWLnzMGx3WF+uM4ZKRls7d6ttw0erIOx06dLFzAE/enz2DG48cbqvzgLnE46zQ/7fgBgb5yVC7PWpEs0Z+ts6lkmB0/mm+tKlywxzSoraVzHcbR2b817294rFWwtObCE+Zvms+fsHrLz9DCym6MbvXx7FSzcblpDLyo5is6Ols/oMwyDx9c9zmtbXmNOnznc2+9eS54EP/6ol6rxtrAnrL544QWdEvHwwzqAmjRJ/356eBR+kMvJ0cONu3frD101mZfZuXNhsPXYY7ow68svF763+PnpHra8PHya+EjOViOXlJFU4QQVdyf3MvO6aousjVhT3N31H84rr6yTy4f49+SQN2Tu3lnucXnRUcS4gp+bf6l9NsqGTt6dORTUTOdf7N5d/IDkZJ3w262b/tQL5hNXAY4c0Z9CKzNNvRre3vo2hmEwOnA0e+P2WmVNvVrh5KRrkF1iwVZ8anzB7LGSlFJmE9BtbWy5K+wu/jj+R0HRU5PnNz5PXGoc9/e/nx8m/kDkPZGcf/Q866evZ0R7vfB7gJuuYxV10fK8rdy8XO5acRcv//0yd/a+k7fGvFXuyg8Fdu3S/wcmT7b4WvWGjQ18/rmuvzV1KsyZo3uX5s/X+w1DL2C9erUedhwzpmbb06mTDrZeeklPEJg9WweCJv7+erZiYiI+TX0kZ6sRy8rNIj0nvc4DKUtIsFVTpkyBp54qvhRGLQrpPJRcGzi0/89yj0uIP0GODfi5+pnd38m7EztjdrK8vydZ+0oEW6bk+G7ddFFUKDvYMn0SrYVg62LmRRbsWMCk4ElcFXgV5zPO14s6Kxbz9r6khhEzczJJzkouM9gqz609b8XR1pH3t71fsC06OZqI2Ahm95nNyyNfZnLwZAI9A4stbQW65xawOG8rOzebm5fezEfhH/HYoMd4f+z7pc5ZpkWL9BDitddadnx94+wMy5fr/+vvvacDsJ9+0vteeAE++QSefFIPO9a0zp31zOfHH9e5a2+9VbxCvWlmdVQU3s4yjNiYmarHW1x6pQ5JsFVT5s8vLDpYB0Ja6byQvSe3l3tc9AX9h6asYGt42+GcTT3L1f5/8qn36cLyDsnJem0zZ2c9jOjvrwt3Hjli/kKmYKtjx0q/lsr6ZMcnXMy8yIMDHiSkeQhAw+rd8va+pHq2TH8MfZpWPtjyaerDlJApfLHrCy5mXgRg9ZHVAIwNGlvuc4sOI1YkOTOZa3+4lu/2fseLI17kxStetKxHy2TTJv3/pKENIRbl4QHr1umg67//1R+2fv1Vf6icNg2ef7522nHjjTqw+/13XfS1ZI6oaV3J6OiCnq0G839fVEp5i1DXNxJsNVIdvTpiZ9iwNzqi3PpX0em6Dm1ZwdbtvW/nwqMX8LZzI9wXPRU8K0sXUoyI0HkoLVroN7z27cvv2WrVSldJr0E5eTm8tfUtLmtzGWF+YQXB1ofhH+L5iicRsRE1en2r8PK6pHq2TDk1VenZAp0on5KVwle7vgL0AtMBbgEF//ZlcbZ3xtPZ02zP1u6zuzmceJiUrBQmLZqE96verIxcyQdjP+CxwY8VPzg3V/dc3Xln2etanjhRONTekHl4wNixesYhwPTpOmn93XctX1C6upo318HeiBHmJ+MU6dnyaeJDTl5OwWLFonEpb13E+kaCrUbKwdaBTm7t2OGTA199Zf6gzExiDF2wsKxgC/QvcjefEPa0QOee3Hqr/qOyYIGefWTSoUP5PVu1MIS4eP9iTiWd4sEBDwK656N50+YsObCECxkXWH54eY23odousZ4tU05NVXq2APr69yXML4z3t79PenY6a46u4arAqyzqeTJXays1K5Vhnw+j+wfdGbBwAEsPLOWusLv4e+bf3Bl2Z+mTLFumc7E++kj/3yi5TFZ2tl6CqSZm59WVrl11Zfjz5/UKEu716I+dr69+LFLYtGje1htb3mD8d+PromXCykxBtAwjijo1ttv1/N4eor9413yNnL17ic6f8W5aQ6os3VuHsbc55D3zf/D11/Df//JdH2fav9WeuNT8VZoCA3XPVslrGUatBFuGYfDa5tfo5NWJsR0Lh5BMPRxezl5sOrWpRttgFV5el1SwZRpGtLhelRl3hd3F/vj9TFo0ieSsZKZ2t2wWsLlaW9/s+YbzGefp1qIbB+IP8O313/Lm6DcZ0GqA+ZNER+vHb7/Vy1GVXFMwKkpPDjE3S7ehUkoXVnV2hnstmI1Zm+ztde9X/jAiFP6OrT26lgfXPMivh3+1eh7n9ujtBUPZoubl5uXKMKKoH27vfTu5NrCw6WHYvLn4ztxcuOceor0d8XbyMrtielHdmncn1QGO552Du+9mzZQw/vPzfzh+4Thbz+QvC9ShA6SmwtkSS6hER0NKSo0HW3+d+ovwmHAeGPBAscTlJ4c8yafjP2Vy8GQ2n95cqSKYdcLbG5KSLpnFqKs7jAhwQ8gNeDh5sCJyBZO6TmJom6EWPa+tR1t2xOwg+P1gZq+YzaJ9i3h769v0bNmTf2/7l/iH45kcXMEMwoQEHXxMnqxLO8yfDxeL/NE9eVI/NqaeLYAXX9SpBC3L/6BWJ/z94eTJwvURU+OJuhjF1CVTaebcDIBtUduqdOqI2Ai+3PUlO2J2FCwB8/3e7+nzcR/e+uct67RflCs7Nxu/1/14+e+XARlGFHUs0DOQEa2H8XGYIvejD4rvXLgQtmwhun9X/NxLl30oqVuLbgDsnjmW8Menc/2iiXTy0vW7dp/Nn6VY1ozE7flJ+jUcbP15Us+8vKnbTcW2D283nFt63sKQ1kNIyUphV+yuGm1HtZmSqM/lVzvOy9OFGjc1gF65KohPi8dW2Rb8EayKJvZNuK3nbbg4uPDala9Z/Lz/u+z/eGnES7R2b80Xu75g8uLJ7Ivfx9x+c1FKWdamhARo1kznD738sl7Y/bnnCvc31mDL1bVWJrxUyeWXw5o1eB/Q9z4mJYYpi6eQnpPOmmlrsFE2BctAVdbslbOZ/vN0ei/ojcuLLnR6txPTf9ZLqB2/cNxqL0GULS41jrjUOP6N+heQYURRD9zR925Ouxn8Fv5D4R9v0NWsO3Qg2sO23Hwtk2CfYBSKZYO9uer7q/F09mTNzWto69GWPXH5JSBMCcAl87b+9z/9SXPQICu9KvOOnT+Gn6tfQeX7koa0GQJQ5aHE3Lxcvtz1JaeTTle5jRYpWkU+Pl7nxd16a+3N9qpl8anxeDXxsryMQhnmj5jPkXuO0Nq9tcXPaenSkkcHP8qqqas4/+h5/rn1H7669itu7n6z5RdOSCgMkPv00eUP3npLTyaBwmCrVSvLzymq57nnoHVrfObqyQzP/fkcf5/+m4+v/pjefr3p6tOVbdFV69k6eeEk4zuNZ9GkRTw15ClCmodwdcer6eTVqdprbQrLlKyd5upQ+RUgapsEW43cNZ2vobmjJx91L54ovyBrC1dMSOJU0in8XCoOtpo6NKWDZwe+2PUFOXk5/DbtN/xc/ejWvFthz1bbtrqi9IEDhU/ctEl/PfIIODpa+dUVd+z8Mdo3K3uR3wC3ANp6tOWvU3+Z3X/m4pkyhxbOp59n3HfjmP7zdP635X9WaW9RhmEw9tuxfBz+ceEf7qVL9fJG69bpYDW+cdYLik8ru6BpZTjYOtDCpUWVn29va0+/gH5M6z7NbBHVMhUNtkDXnXJ318U2DUPPRGzZUhesFbXDxQVefJEm+yNxtnEkNiWWOX3mcEPIDQD08evDtuhtlS4JkZOXQ2xKLN2bd2di14k8d/lz/DT5JxZPXkxn787FCuQeiD9AeHS4VV+W0IoGW64OrpX7/1pHJNhq5BxsHZgZNovlneDMl/mJ8jk5/OoeyzrXBOJS4yzq2QLo5dsLZztnlt+4nM7eekiwe4vuHE48TEZOhq6zFRICO4tUrZ8/H3x84LbbauLlFVNRsAXQo0UPDiQcMLvvkbWPMOrrUaWWhtkXt4++n/Rl3bF1eDh5cDjxsNXabJKSlcLKyJXcueJOfsvNX2T3qad0NfmtW2H0aIiLs/p164P4tPgqz0SsF0oGW15eurr5xo06af7kycaVHN9Q5Kc1tHNoTl//vsWGl/v49SEhLYGTSScrdcqzKWfJNXILCuIWVXRma05eDuO/H8/ob0br90ZhVaZga3af2UzoPKFuG2MhCbYuAbf3vp08BQtdj8Bff8GJExz0LPxE5+vqa9F53h79Njvu2FFsVla35t3INXI5EJ8fwPTqBTt26KBu2zY9XPnggzW+GHdmTiZnLp6hvUf5wVZHr44cOXeE3LzcUvv+OfMP5zPOc/x8Yd7Fzwd/pv/C/iRnJrN++nquaH8FR86VUd6iGkyzpWyUDTN3/1f3jNx4I4SH694tHx/ds9UIizMmpCVUayZinSsZbIEe9u3bV//uHzzY+PK1GoL8f5Pfve7nj//8gaNdYc96H/8+AKw7tq5SpzTNXDUt9VSUv6s/FzIukJadxo/7fuTIuSMkpCXww94fqvoKRBlMwdbTQ5/my2u/rOPWWEaCrUtA+2btubLtCD4JU+R89AGZ+/dwrBncFXAt13W5jhHtRlh0nhYuLQp6tEy6t+gOUJi31bu3/uNz5oweTvHw0Oum1bATF05gYFTYsxXkGURWbhanLxbPu0pMSyxIbt0Rs4M8I49nNzzLtT9cS1efroTPCmdQ60EEeQZx/MJxUrNSmbZkGm/985ZVPrmaymeE+YURnRpDVlyM7hVxzc9FaN5cz05MSqr2teqb8tZFrPcMw3ywZWOjl7WJi2t8NbYaCh/9O+V7PoemDk2L7erZsie9fXvzxB9PkJhmeQFhU8+VafWBoky9XaeTTjN/03xCmofQxbsL7/z7jlSwtzJTsOXp7FnHLbGcBFuXiDv63s0ZV4NVEYs4unUVeTYwuOtofpr8E528O1X5vEFeQTjaOhbO8OvVSz9+8QX8/LOuwePmVv0XUIFj548BVBhsdfTSs6dKDgUWnZkUHhPOfavv47k/n2NG6Az+nPFnwRtpoGcgOXk5fLf3O77Z8w33/XYfPT/qWanFjM0xlT/o4t0FgHNZJYKq5s31Y10OJZ45o7+sKDcvl3Pp5xpusJWaCpmZ5pfhCQuDO+7Q30uwVfuaNtV5cmZyHW1tbFk4fiHn0s/x6O+PWnzKinq2AFZErmB//H4eHPAgc/rOITwmnK1RW6v4IoQ5CWkJNHNqhr1t3aw9XBUSbF0iru54NS0dvfmoRw4HV+pu105telf7vHY2dvQP6M/vx3/XG7p315/q583TSapz51b7GkVdzLzId3u+Y+6qucUCpOoGW6aZSR2adeCP43+wIHwBt4TewqfjP8XJrjCxOcgzCIAvdn0BwHfXf0fUxSiGfj6Uc+nnqCrTMKIp2Co528b0Kb1Og61p0/TwmBUlpidiYDTcnC1T8dmy1jycP18PB48aVXttEppS+t+ljIklPVr24Pou17PuuOVDiVEXo3CwdTA77G36QLbkwBIALm97OTd3vxlXB1fe+fedKrwAUZaE9IaXeiDB1iXC3taemX1msSoI1gRkAlSrR6uocR3Hsfvsbk5eOKlzs7p00UNed98NntXv5s3IyeDziM+5+rur8XnVh5uW3MR7295jwMIBvL/tfUAHW852zhVWwm/p0hIXBxciEyOLbd8WvY1OXp0Y1nYY26K3kZmbyew+s0st+RLkpYOtv079RVefrtwQcgM/Tf6JY+ePseZoGeviWcA0jGgapi01tGHq2TL94Vi6FC67TNfgqg2GoQtYWrln62yKLoDbYHu2Kgq2PD31cHBjWBexITLlOpahnUc7oi5GlZoUU5YzyWfwd/U3uxSUqWdr8+nNtGjagtburXF1dOWW0FtYtG+R1SvWX8oaYp6nBFuXkNt7346hFJ/0goCcpmXWo6qsqzteDejuc0AnBjs5wQMPWOX87/77Lrcsu4XdZ3czu89sNt2yifiH4xnebjgPrnmQsylnOXZBz0SsaD08pRRBnkEcPlfYs5WWnca/Uf/Sx78PvXz1MGhI85CC74tq0bRFwX0bGDAQgKFthmKrbNkXt6/KrzE+NZ4m9k1o46GHm0r1bJUcRvztNz3brbZ6umJjdb6YlRfIXrR/EQpVkLDc4FQUbIm65eNT7tJXAW4BZOdlFwT9FYm6GGV2CBHA1dEVN0c3DAz6BfQreC+a3Xc22XnZLAhfYPZ5ovIk2BL1WluPtoxqdwW5NtDJvfzhtsro6NWRQM/AwkWeX3hBLw/Uouo1j4o6eeEkbo5unLj3BK+Pep3BrQfj6ezJu2PeJSs3iyfWPcG2qG0VDiEWbW9kYiSZOZm8s/UdOrzdgdiUWMYGjSXMLwyAGT1mmA3clFIEeuop5YNa6yKtjnaOBHoGsi++6sFWXFocPk188HLWBU1LBVumP+am4OqYHjYtKJhp8thj8MwzlW9ARoZeUPl4GRWwTbXTEhOtNiMyMyeTj8I/YlzHcRb/29U7EmzVb+UMIwK0cteFZkuuj1mWMxfPmC37YGLq3err17dgW0evjozqMIoPt39Idu6lsQRXTZNgS9R7d/S9G4DOXS1bO84SSinGBY3jj+N/kJmTqQs49uxptfPHpsbi6+JrdkhvSvAUPo34lPMZ53lggGU9aaYZhUHvBDF39Vw6enVk44yN3BByA338+rB0ylLm9J1T7vMBBrUqrIgf3Dy4WsFWfGo8zZs2x6uJDrYS00v0IDk46Jmdpj8c5oKtU6fgtddgyZLKN+D772HCBGjfHiZO1GtZFmUKtnJyiq/7Vw0/7vuRuNQ47ul7j1XOVyck2KrfKhhGNPVSlZydbI5hGEQlRxHgar5nCwrztvoF9Cu2/Z6+9xCTElOQz2WSlp3GcxueY9Cng+j2QTdav9Eaj5c8aP5qcxl2LINhGBJsifpvXMdxTA6ezMSuE6163l6+vcjMzayRtcFiU2LLrAX23LDnuCroKjZM38CwtsMsOl9P357kGXn4ufqx9ua1bJi+oWApH6UUEzpPKFaTp6QrO1zJgIABBT1coJczOnLuSJXLQMSlxuHT1AcnOyea2jct3bMFeigxLk4vIm4KsooGW++9p/dFR1e+AabzPP20zgcbOFBXPjcpuiqAlYYSVx5ZSYBbAFe0v8Iq56u0FSuqPwybkKDXRHSv/wvhXpJ8fCA5Wc8YNaOVm+U9W+fSz5GRk1Fhz5ZC0cev+LD46MDRtG/Wvlii/MXMi/T4sAfP/vksoD/EjWg/glGBo4hPiy9cmUMUk5adRkZOhgRbon6zs7Hjh4k/WByYWMoUeNREwc/YlNgyE9+DvIJYcdOKSuX8XNv5Wg7OPsiWW7dwRfsrKszzKum2Xrex+dbNxZ4X7BNMnpHHoYRDlTqXSXya7tkC8G7iXbpnC/Qfjrg4naSek6O3mYKk1FT4+GM9E/TcOUhPr1wDoqN1MDdvHqxaBadP63X+/tSLe3PwYOGxVgq24lLjaO3eutL33ypOndJrTn7wQcXHlichQVeMt5G30nrJ1ONYNG/rzBnYsEHvbuKNo62jReudlldjy2RG6AyeG/Yc7k7Fg29bG1vm9JnD36f/5ueDPwPw/rb3OXLuCMtvXM7fM/9myZQlfHbNZ7w2Ule6P3HhhGWv8RJjmrktwZa4JHXw1LOtjp47avVzx6bE0rJp+bMMK0MpRSfvTlb9Ix/cPBigSkOJhmEUK+zp3cS7/J6tonlVpmDrq6/g/HmYOVP/HBNTuUZERYFf/rJNV16plwjy8oIrroCPPtI9W0F6+LS8hOPKqNNipqtW6cdTp6p3HnMFTUX9YSqZYhpKTE7Wv9NjxkBWFkopAtwCOJNccc+WaVivvOXNhrUdxtOXPW1239197qa3b29mLpvJv1H/8vqW1xnVYRRjO44tdpyfqx92NnbFVrIQhUzvjRJsiUuSTxMfXB1crd6zlZKVQkpWSoUlHepaR6+O2NnYsTdub6Wfm5yVTGZuZkHg4dXEy3xV6+bN9R8NU75WcLAOFvLy4K23dPX+SZP0vqhKFlmNji4MtgA6dtQB15VXwp136v1D9FCrtXq2rLUAdZWsyJ85W51SFjk5cPiwBFv1WdFgyzBg1iw4dEhPCNmjV71o5d7Kop4tU7BV1cXOHe0c+X7i9+QaufT7pB/xafE8OeTJUsfZ2tjS2r01J5JOVOk6jZ0EW+KSppSig2cHjp63bs+W6Q2uvgdbDrYOBHkGValny1Q9vugwotmeLdM09iNH9LDVkCG6Z2vtWj3Md9994J8/xFHdYAt0HtIvv8Ajj+ifx+Z/ArdCsGVKcrW4mKlhwE8/wVEr/H5lZMC6/EKWlb1PRdtzxx36D/b06dVvk6gZRYcRP/hATwSZNUtv26YLGQe4BViUs2WN96JAz0D23b2P9696nzdHvVmQK1pSO492MoxoRp6RV1CTUIItcckK9Ay0es9WQwm2IH9GYhVqbZnePEyBh5ezV9nDiHl5usepdWtdKDMpSedZtWwJkycXBkyVSZLPztbDk/5mclFsbeHll3Ue2DXX6KrcVgi2LmRcICcvx/Kerb179SzJoCB41PLlVczauBHS0iAwsGo9W7m5cPvt8Omn8H//Vzh0K+ofU8/WypX6w8hVV+mgy8urINhq5daKqOQos4vTF3U25SxN7atfnzDALYC7+tzFvf3vLfOYth5tJdgqwTAMenzYg5nL9P83CbbEJatDsw6cuHCiwjetymhQwZZPMMfOHyMtO61SzzMlfBbt2UrKTCpdk6dvXx3s/PGHLtHQurXevnmzrtZvKg/h7Fy5HpuzZ3VPTcmeraKaNdOBl6enVXK2TK/Z4p6tvfnDs4MG6fIW1cm12rxZ38ebbtLBaskyF+XJytLL7yxcqGduPvts1dshal6zZvrf+uuv9e/3V1/pXuGwsGI9Wzl5OQUfesoSmxpb5SHEymrr0ZbYlFjSsys50aURO5x4mL1xexnQagC397qdZk7N6rpJlSLBlrCaQM9AsvOyS9WsMQyD8OjwKp3TFGyVVfqhPglpHoKBwcGEgxUfXERBz1aRBHmgYK3FPCOPT3d+yqaWWfBO/tTx9u0LFzd2cChc8Fgp/UelMj1bpmPLC7ZMvLzK79kKD9cBSQVMQ6cWfzrdv18HewsX6p8/+siy55lz9Ci0alWY8G9pYJqWpnv3Fi3SAd+8efp+i/rL1lb/ztrbw48/Fi4f1qcP7NsHaWkF5R9GfjWyYPkvc8qbFW1tbT3aAnAqqZoTOBoR0xqWn13zGQuuXlA3s5irQYItYTUdmukZiSWHEj+L+Iywj8P4N+rfSp8zNiUWW2VbUFm9Pgv2yZ+RWMmhxJMXTmKrbAveyE2vNTE9kfjUeMZ+O5Zbf7mV5zc+D7Nnww8/wMMPQ9u2+gRTpxYu5wN6OLAyPVumY6sbbP3yi+4x+M9/KqwybxomtXgYcf9+PezXsaMu2fDxx2XWTqrQ0aN6CDYgvzilJfcqOlovJr1mDXzyCTz4YNWuLWrfQw/pHq2+hVXd6dNHD8nv3MllbS/j9l6342jnyJyVc/j92O9mT1MXwVZN1C1sqP44/get3FoV/J1paKodbCmlPJVSa5VSkfmPZfbtKaXclFJnlFLvVve6ov4xV2srJy+HFza9AFClIn2xKbE0b9ocWxtb6zSyBgV6BmJvY1/pJPmDiQdp36x9QSFVU2/PkgNLCP0olPXH1+Pv6l8w9MbkyTroaNECvvtO51QVVZM9W97e5ocRMzLg/vs527wJxg8/6J6fclR6GHH/fujaVX8/Z46eXbZokWXPLckUbJly1MrL20pIgGHD9LFbt+oE61tvrdp1Rd149FGYMqX4tgEDdI/wm2/i5ujGgqsXsHHGRrr4dGHakmlmq7efTTlr1RI05TEFW5K3peUZeaw/sZ4R7Uc0uB4tE2v0bD0GrDMMIwhYl/9zWZ4HNlrhmqIe8nfzx8XBpVjPzg97fyiYoVjZ4TWAmJSYBpGvBWBva08n706VD7YSDtLZu3PBz6Yle55e/zRN7Zvyz23/MDpwtPmckhtuKEwCNjH1bFm6hmF0tB5uKdo7VhZTz9bOnfDii3DXXXqWYrdu/JVzDL+7M3hwVht4/fVyr28aRrSoZyszEyIjC4OtESN0sPnee5a8uuJSUvRkgPbtK565GRenazJt3Qr//S/s3l1YWkM0bD4+eg3RxYsLlrdq6tCUHyf+yMXMi0xbMq1Y7mlWbhaJ6Ym1lrPl5+qHvY09L//9MmO/HUtOXk6tXLe+2hW7i3Pp5xjRbkRdN6XKrBFsXQN8kf/9F8AEcwcppXoDLYA1VrimqIdslA09W/ZkR+wOQH8aeeGvFwhpHkK35t0qFWydTjrNnJVz2Be3r8EEW6CHEiszjJibl8vhxMPFgq027m3wcPLgxpAbCZ8VTmjLUJo3bU58ajyGJQGUn5/uabpwocJrf737a3Kjz4Cvr2VV0L28dBAyZAg88YTuXYqJIbdrF+65PQClFG/4neTLFrHFl/spIT4tnqb2TXG2d9YbjhyBX3/VPVglq99HRuoZgKZgy8ZGTwj45x+dI1YZphplHTpAkyY6gdpcz9amTRAaqmsyLVsGTz4JnTuXPk40XA8/DCEhMH9+wabg5sG8e9W7rDu+jhf/erFgu+mDTm29F9koG8Z1HEd6djorI1eyP35/rVy3vjLlaw1vN7yOW1J11gi2WhiGYSpXHYsOqIpRStkA/wMessL1RD3Wy7cXEbER5Obl8vPBn9kfv58nBj9BV5+ulQq2nvjjCd7b9h4nk06WW7G5vgn2Ceb4heOkZqVadPyJCyfIys0qFmw1c25GwsMJfHv9t7g6ugK6Byg7L5ukzKSKT2rKRerQAd4vO+H3t6O/cfPSm1mfus+yIUTQwVZWFmdsU/nulxd4+eeHmfPfgVxxXTIRuWf48tov6d+sO88MA/7+u8zTxKfFFx9CvO02GD9eF2pt0kQnsA8bprd/9pk+Jji48Pjp06Fp08r3bpnqdLVvrx8DAkr3bKWnw3XXgYuLDuiuvLJy1xANg709DB1afEUG4JbQW5jWfRrPbHiGz3Z+xkNrHuKvU38BtTsresmUJfw5Qy+XtSNmR61dtz5ad3wdnb07N6i/BSXZWXKQUup3wNxvWbHyt4ZhGEopcx+97wZWGoZxpqLxVqXULGAWQGvT1HbRYPTy7UVadhoHEw4yf9N8gjyDmBw8mUOJh1i0fxEZORk42TmZfW5iWiKzV85mRLsRfLvnW+7pew8DWw2kn3+/Wn4VVWdatudAwgHC/MIqPN4UgBYNtoBSOWqmshBxqXF4OHmUf9KrrtLDXu+9p+sL3X232cMOxOvFpU+nxYBfX7PHlOLtTao99J7jQNyOJwBo5tSMVu6teGjAQ9wYciNnk2N44PxDRG9Zg9+0aWZPU2qpnqgoPTw4c6YOiI4c0Y9LluhliGxs9NChiYcHTJsGX3wBr76qg0BLFO3ZAh1slezZ+u47nau1aBH06GHZeUXDFBCgf79SU3Xwji7Q/P5V7/Nv1L/M/EXXdDL9ka/tXvYgryBcHFzYEbODGaEzavXa9UVWbhabTm5q8K/fomDLMIwrytqnlDqrlPI1DCNGKeULmCtWMgAYopS6G3ABHJRSKYZhlMrvMgxjAbAAICwszMKkE1Ff9PLtBcALf73AjpgdLBy/EFsbWzp5dSLPyOPIuSOENA8x+9zF+xfzw74f+GHfDzjbOfPkkCdrLUfCWorOSKxMsNXJq1O5xxUNtjp6dSz3WFxc9LDX1q3l1qM6lKgXzY7OPgdtLPzE2LYtn/WEOIcslk5Zyoh2Iwp630wG5VfF/vv4n5SV4RSfFk+LpkX+bePj9Xp1N91U/MC0NJ1sn56u64cVNXu2LgHx6ad6SKgkwyhdmuHoUR2oNcufx9O6NaxerZc6GjZMf731FnTrBpddVt6dEI1BK132gTNnoFPh/0FXR1dW3LSClZEr+evUXyzarydjFPudrQU2yobQlqGEx1StdE5N2hW7i6UHl5KTl0NMcgxjO47lui7XWf06/0b9S2p2aoMeQgQLg60K/AJMB17Kf1xW8gDDMKaavldKzQDCzAVaouHr7N0ZZztnvt3zLa3dWzOt+7SC7aCDi7KCrZVHVtLavTVTu02lfbP2DS7QAr0gt4Otg9kk+fjUeEZ+NZJO3p24rvN1XBV0FQcTDuLTxKcgKb4spiE3U2K5RQICdAHPMhQEW3YZ5qvHm5EzfBivT27FAI8AJnSeYPaYni174ow9m41TTEpK0sv+FJWRQfzRPYS0yX/NWVm6uGjJRH/QQ4r/93/mG9Otmx4G+uADeOABneRv8uij8O67umeqVy8dTPXqpdcy7FBk6vhTT+l8tQ0bdE/g66/r7R9/LDW0LgWmYOv06WLBFujZxXP7zSWkeUhhsFUH70m9Wvbik52fkJuXW69mZT+/8Xl+OvATCoWtjS0HEg7USLC17tg6FIphbYdZ/dy1yRo5Wy8BI5VSkcAV+T+jlApTSn1ihfOLBsTOxo4eLfXQyyMDH8HB1gGgoDemrLytzJxM1h1bx9igsbww4gVu63Vb7TTYyuxs7Ojs3dnsgtR/nvyTXWd38duR37jhpxvwftWbH/b9UGoI0ZyiPVsWCwjQMwdLJpznO5SQH2y5YnHO1voTGziecpoHB5RdZ8re1p6+bl34uxUQEVH6gMOHSbDPxic+P6/NVErCXLBVkTlzdM7N6tWF2wwDvvxS91rZ2emhxpkzdcL7unWF+Vqg79Ezz8D69XpCwYYNsGCBrHd4qTDlN5ZT/uOyNpfh5+qHh5NHmSkQNam3X2/SstM4nHi41q9dnqjkKK5ofwV5z+QxtdtUi9aXrIo/TvxBL99eeDp71sj5a0u1gy3DMBINwxhhGEaQYRhXGIZxLn/7dsMwSv3FNAzjc8Mw5lT3uqL+GtZmGG3c2zCzZ+GacU0dmtLavXWZs2o2ndpEanYqYwLH1FYza0ywT7DZnq3w6HDsbeyJfjCajTM2MrvPbFq6tOTqjldXeE5T7a1KB1tgtrTBhYwLnE09q3e7YXGwZapoXdEQ6SD/AexsCWmnj5Xalxq5j3R78DHNIYjP762rSrA1YYJu+7tFSvdFREBsLDz2mF4HMSlJL9T9zTe6x+uhMubpODnpocPbb9fJ06LxM/Xonj5d5iG2NrY8OeRJbgi+oZYaVZwpNaO+DSVGJ0fj66JX9ghwCyA6OdqqS7UBpGalsuX0lgY/hAhSQV7UgP8O/y8HZh8onNafr0eLHkTERph9zqrIVTjYOjSK/1TBPsGcSjpFcmZyse3hMeGENA+hiX0ThrQZwuujXufwPYd5eJCZfKMSHGwd8HDyKCxsaolyPrWberW8bF0r1bOVmK6rx1e0zM6AoMvJsYWdZpZpOnlUz6wKSMrTG6oTbNnbw6xZumfrSH4x3VWr9OPo0frRxkYPEd10E7z0UvFK4uLS5uSkf+8qWJD87j5388G4D6x//eTkCuvhdfbujL2NPXvO7rH+9avIMAxiU2ILgq1Wbq3INXLNFoMtKS41jmlLpnE25WyFx/516i+y87IbdH0tEwm2hNXZ2tiWCrRAf0I7mHDQbFmElUdWMqztMJo6NK2NJtYo04zEPXF7CnqiDMNge/R2evv2rvJ5mzdtXrWeLTOf2k35Wper9sS6QG5Ly3JREtIScLR1pIl9k3KPa+en78GZcydK7TsarYdYO8TlF2qszjAi6GDLzq6wzMXKlXrZoBYNL+dP1IFWrcrt2aoxJ07ofMGBA+Hbb3WJkzff1GtuvvSSri2HTk1o36w9R84fKfd0telc+jmycrMKZmkGuOn3GkuGEv84/gff7PlGLz9mwbH2NvYMbj24eg2uByTYErWml28vDAx2nd1VbPvx88c5mHCwUQwhQuGMxGu+vwa///nxyNpH2B+/n/MZ5y2aoViWKgdbZfRs2dnYMTjVk1wbiHe0rEJ1YloiXk28Klwyw9dNvwnHJJdeNujoeT202OFMmt5g6tnytnBR6lIX89V1sT7/HA4cgC1b9MxGISwREFA3wdYrr+jJIceO6fVNZ86E++/XOYSPPw7bthUcGuQVVGrNWUv9tP8nQt4PqdIKHmWJSdGlNX1dC4cRwbJg63SSvtcLwhdw/Hz5az+uO76O/gH9G8WHcAm2RK0x5R6ULNC36oge9rkq6Kpab1NNaN+sPU3sm5Calcr4TuN5dfOrjPxqJKCTXavKp4lP5YKtJk3A01MHWyWGKvbF76N9s/a0SdBBVnRKjLkzlJKYnljhECLo2luOuYqYjNLrKB7NisU1E7yjzukN8fF65p9nNRJg77pL10saPlwPDc2aVfVziUtLq1YVDiNaXXS0Lllyyy26HMmuXXqih2kpLCi2AkNgs0COnDti2QoS+QzDYN6f85i4aCL74vex+sjqip9kafPzP0QVDCO661mdpy9WHLSeuXgGJzsnbG1see7P58we8/yfz9Ph7Q7siNnRKIYQQYItUYv8Xf3xaeJjNthq36w9QZ5BddQy67K1sWXV1FXsuGMHS6Ys4YsJXxCTEoO9jT3dmner8nmbN21euZwt0J/aDx6ENm0KhtkyczJZd3wdl7e9HL9YPaQbdbGM9QFLSExPxMu54gKiSil8c52Jzi1R8T47m6O2F+lwDlRCog4C4+N1UVLbakxrv+wy6NJFJ8Y/+WRhr54QFWnVSs9ETUmp+Wvl5MCMGRAYqL9/9FFdF697d2jbVn/gCAzUxxYNtjwDSctOK+hRqkhqVipTFk/hmQ3PcHP3m2netHmpEYXqiEku3rPVzKkZznbOlvVsXTxN+2btmd1nNl/t/qqguHJRK4+sJCEtAe8m3jVSTqIuSLAlao1Sil6+vYoFWxk5Gaw7to6rAq9qsKu5mzO0zdCCkg7/6fEfPr/mcx4b/BiOdo5VPmfzps1JSEuo3IyfgAD44w89TPLVVwBsOLGBlKwUxncaj9+p80DhJ9WKJKQlVFgTzMTXxp0YmxL5eadOcawZdMh1g+xsPVMwPr7q+VomSsGzz8KoUbrmlhCWMgXmX30F587V7LXmzdOlSKZO1etvFi1DYuLioofUiwRbQV76g6glQ4kxyTEM+WwIi/cv5tWRr/LFhC/o2bInu2KtGGyZhhHze7aUUgS4BVgcbLVya8Vjgx+jiX0T/m9D8Tp6hmFwKOEQN4XcRNzDcXRrUfUPqPWJBFuiVvXy7cW++H1k5mQCsPHkRtJz0hkT1LhzbKaHTmfe5fOqdQ6fJj7kGXlVm5GolK4oHxvLL4d+oYl9E4a3vZyWR8+iDMuDrcQ0y3q2AHwdPIlxztVLoeTLPXKY4x7Qwa2N3hAfb51gC2DyZD0r0an2ayGJBiwkv8jy3XfDgAF6hmBJmZlw8WLZ5zAM+OkniCmn52nLFr2M1owZumjugAFlH9u2bameLbAs2Prvxv9yIOEAy29azkMDH0IpRY8WPdgXv4/s3OwKn2+JmOQY3BzdiuVStXJvZdEw4ukkHWx5N/HmwQEPsnj/YsKLzFpOTE/kfMb5ilfKaGAk2BK1qpdvL3LycgqKfq6MXImTnVODrw5cG/r690WhmPXrLHLyyk5oP5RwiG4fdCNsQRiL/C/ojU89BYaBsXw5vxz+hVEdRuGUno1dShotbFwtCrbyjDzOpZ+zKGcLwM/FV5eVKPIHKCpyB1l20KF1qN6QkKC/qpocL0R19eihh58XL9blQ+66q3Q5hrvuKn/5pjffhIkTy18Y/eWX9XD5O+9U3Ka2bYstkN3avTX2NvZEJkZW+NTfjv7GyPYji+XAhrYMJSs3y2pJ8tEphTW2TCzp2crMyeRs6tmCHK8HBjyAp7MnT61/quAYU1maTt7lL2HW0EiwJWpVyST5lZG65ENFpQQE9Avoxztj3uHXw7/yxpY3yjxu8+nN7I3by774fXzjl6iLeP7f/0GbNkT8/jVnLp5hfKfxOkkX8HPwIiq54pytpIwkco1cy3u2PFpxwRnST+f/0YiO5ui3uvhoh475i4tbs2dLiKpq0QKuv14PRX/zjS7DYJKcDN9/D4cO6SAsNxf27dPbnnoKxo+HB/NXVChrVuOJE/Drr3rihotLxe1p2xZOnoQ8XYvOzsaOds3aVVj+4ei5oxw9f5QrO1xZbLtpVY+y6hxWVkxyTEG+lkkrt1YVFjY1fahr5aaDLTdHNx4b9Birj6xm08lNAAWV8qVnS4hqaOfRDndHd3bE7ODIuSNEnovkqsDGMQuxNszuO5uOXh3ZGrW1zGNMgdOAgAGcybsAr76q61CNH88viX+jUIwNGlvwh8HPxdeini1TQVOLc7aa63yU2DMHdS7MqFEc1QtM0KGVfvPn7Fk9A0uCLVEfPPEEjBihl4Hal78KxNKlesmr9HQdeE2dqoceb7xR18M6elQHUaGhZldrAPT6nUrBnXda1o527fTQ5dnCwp+BnoEVDiOuOboGgFEdRhXb3tGrI462jlZLko9JiSmosWUS4BZATl5OudcwDTOaSkWAfk/zdPbk4x0fA7oGoL2NPW092lqlrfWFBFuiVhUkycfuYGXkSoBGn69lbR2adeD4hbLr00QnR+Pp7EmgZ2DxHIrx4/mlfQ4Dm3bWC1sf1p8g/XzaWxZspVlWPd7E108PA0Sf3ANjx3LxxCE+uL4Nbo5utGqbH2wdPqw/vUuwJeoDW1v4+mtwc9M5gKmpuqfLJDZWl2YYOlQvC5WaqoOyDz/UC5ybC7bS0+GTT/TSUqaFryvStq1+LJK3FdoilN1nd/P3qb/LfNqaY2to69G2IMfLxM7Gju4turPlzBbLrl8OwzB0z1aJYcQR7UbQzKkZgz4dxOtbXjfbw2WqsWUaRgRoYt+EUR1GseboGvKMPA4nHibQMxA7G7tqt7U+kWBL1Lpevr3YFbuLj3d8TI8WPUq9MYjytfNox7HzpdccNIlKjsLf1Z8AtwDiUuMKJiOcCW3PDj8YH5U/jHHwILi44N8iiPi0eLJys8q9bkKarpll6TCin68eBoj58VMywrcy4ZlO7Eo7xjfXfYOti6uuA2bqPZBgS9QXLVvqgOvAAd1btWZNYTJ7bKyuydW7t871ciwyu9jf33yw9d13umf3nnssb4OZYOuRQY/Q1qMtNy25iXPppWdNZudm88fxP7iy/ZVmZ3ZP6DyBzac3c/LCScvbUUJWbhbvbXuP9Jz0Uj1bQV5B7Lt7H1d2uJIH1zzIkM+GFORfmZg+/JmGEU1GdRjF2dSz7D67m0OJhxrdECJIsCXqQC/fXmTmZrI3bi9z+sqa5JXVvll7LmRc4Hz6ebP7o5Oj8XfzL3hDM/Va/Xr8NwDGrzqme5MOHYLOnfFz04vxVrSuWaWHEfPfjE83zeWG53uwPnUvX0z4gnEdx+kDfHzg99/196GhFp1TiFpxxRXw/PO6NMn//R+89ZbefugQpKUVLmBdlL+/HmYsOpvRMHRCfEiI7g2zVJv82bpr1hT8H3F3cuf7678nOjma2365rVSB061RW7mYeZFRgaNKng2Am7rdBMA3e74xu788uXm5fL37a7q814V7Vt3DkNZDmNZ9WqnjfF19+XnKz3x97dccTDhIjw978MfxPwr2n046TTOnZqUqwptyzJYfXs6Rc0fo5NW4kuNBgi1RB0xJ8h5OHgVvAMJy7ZvpXKiyhhKjLkbh5+JXagmNZYeWEWTfkk6HEvVSIIcOQadOBZ9QKypsahpGtLRny6uJF3bY8NwYZ5ZlRPDOmHeY2n1q4QHe3rrW1vDhuiCpEPXJk09CXBw891xhT9P27frRXNFcUwB26hTMn69n4f79tx5uvOcenbNlqaZN9TJUn38OV15ZkLvVx78PL414iaUHl/LB9uILY685ugYbZcPwdsPNnrKtR1uGtB7CV7u/KrcS/fn083wR8QVzVs5h5rKZTFsyje4fdufmpTfj5ujGyptW8ueMP2netLnZ5yulmNp9Kvtn76epQ1O+3v11wb5TF08VG0I08XX1pUeLHjyz4RmycrMY2GpgRXeowZFgS9S6IM8gfF18uTvsbpmFWAXtmrUDMDuUmJOXw9nUs/i7+RcLti5mXuSP438wPuR6lK2tnkl16lSxYKuivK2EtARslS3uTu4WtdNG2dDSzY8kI51nL3u2dC+maehw7lyLzidEnTGtcBCeXw/KXM+WKQBbskTPUnziCXj3XfDw0En1lbVsmS4XYRiF1wXuH3A/YwLH8MBvDxQrVLrm6Br6+ffDw8mjzFNO6z6NgwkH+efMP2Uec+svtzJj2Qy+2v0Vvx/7nS1ntuDi4MIPE38gfFY4Y4LGWFSAuqVLSwa2GliQJ2YYBtujt9O9RXezx0/qOglHW0e+mPAF13S+psLzNzSNKwNNNAi2NrZE3hOJs71zXTelQWrnoYMtc4u4nk05S56Rh59r8Z6tNUfXkJ2Xzfgek2Hofp2wC5UKthLTE/F09sRGWf4ZbVq3adjb2vN/l/1f6Z1duuiclHHjLD6fEHXCxkaXh9izR/9cXs/WkiX68auvdG/W3Lm6p6qy+vSBzp31kj47dsBVeta2jbLh8wmfE/phKFMWT2HnHTtJz0lnW/Q2nh76dLmnvDHkRh5Z+whvbn2TAa3MF1U9dv4YI9uPZPW01ZX6v27OgIABLD+8nHPp57iQcYHYlFgGBpjvtXps8GM8MOCBRvt3QXq2RJ1o6tC02v+RL1XuTu54Onua7dkyBUz+rv64Orri5ujGmYtn+OXQL3g6e+ru+fHjC9eB69QJ7ybe2NvYWxRsWZqvZfLiFS8y7/J55j8Jv/qq/iNSnTURhagtLVtCVv4kEj+/0vtNwVZEhB4it7XVNbnuvrvq13R1hY4d9f+TIpo3bc47Y97hUOIhNp/ezIYTG8gz8krV1yp1OkdXbu91Oz/t/6nMRPmYlBjauLexyvvzgAAd0G09s7VgFuWg1oPMHmtrY9toAy2QYEuIBql9s/Ycu1A62DLV2DL1VgW4BXD0/FFWRK5gbNBYPZ366qv1wUpBUBA2ygZfV98KC5vGp8ZbXPbBIra24Nx431xFI9OihX5s3hwcHErvd3aGZs3098OG6Vyv++/XJSGqo1evYsOIJqY1A6OTowsqy/do0aPC093TT8+KXBC+oNS+nLwc4lPjSxUsrao+/n2wUTZsObOFzac34+boRrBPsFXO3dDIMKIQDVA7j3Zmq0EX9GzlzzAMcAtg1ZFV5Bl5hbOHOnSA4GDdu9VE58z5ufpV2LMVeS6SK9pfYb0XIURD0rKlfjQ3hGji7w/nz0O/fnrlBmvo1UvnWJZY1spU5yomJYbo5GjcHd1LzfIzp7V7azp7d+ZAwoFS++JS4zAwStXQqioXBxe6t+jOxpMbOZd+jv4B/bG1uTR7sqVnS4gGqH2z9py4cKJU4cCoi1HYKlt8mujk8wDXAPKMPIJ9ghnZfmThge+8A28ULvlTUbCVlJFEdHI0Xbxl1qC4RJmCLXPJ8Samff36We+6vfTsbXbuLLbZ1dGVpvZNiUmOISo5qlTdq/L4ufqZ7cmOSdbrmFqrZwtgTOAY/jz5J3vi9jColfkhxEuBBFtCNEBt3NuQnZddqjZWdEo0vq6+BZ8eTUny9/e/v3je1OWXw7XXFvzo7+pfbrBlWsBWgi1xyTINI5bXsxUQoIfHe/e23nVNwVaJvC3QQZGpZ6sywZa/m/n/7zEpOthq6dKyam01Y97l8/hywpeMDhzNDSE3WO28DY0EW0I0QG08dNHDk0nFk1yPnT9W7E13bMexXN/l+uL1rczwc/UjKTOJKYun8HnE56X2m4Ktzt6dq9lyIRooS4YR586FhQsLhuetolkzHehFRpba5etStWDLz8WPmOQY8oy8YttNH96sNYwIeqmgm3vczKqpqxplZXhLSbAlRAPUxj0/2CoyoygyMZKNJzcyusPogm19/fuyePJinOycyj1ft+Y62fb3Y79zy7JbmLNyDtm52QX7DyQcwN7Gng6e1Uz2FaKhsmQYsXt3mD7d+tcODDQbbJmG/ysdbLn6kWvkEpcaV2y7aRjRmj1bQpNgS4gGyFzP1jv/voO9jT139bmr0ucb23EsKY+nEPdQHA8NeIj3tr3HqK9HFVSNP5BwgCCvoEa3OKwQFuvVCyZN0kv51LagIDhypNRmXxdfjp0/RnZedqWHEaF0bb2YlBg8nT1xtHM09zRRDRJsCdEAuTi44OnsyamkU4BOYP8s4jNuCLmhyp9Kmzo0xdbGllevfJUvJ3zJ5tOb6fNxH/bG7eVA/AHJ1xKXNldX+PHH8nu2akpgIERHQ2pqsc2+rr4FQ4GV7dkC88GW9GrVDAm2hGigWru3LujZ+nTnp6RkpXBvv3utcu6be9zMnzP+JCMngwELB3D0/FEJtoSoK0FB+vHo0WKbi+ZWVSXYKrkeamxKrFXztUQhCbaEaKDauLfh5IWT5Obl8va/bzO49WB6+1lvFlS/gH5su30bXby7kGfk0dWnq9XOLYSohMBA/VhiKLFoiQZ/V8t73Fq6tEShSvdsJcdYteyDKCTBlhANVBv3NpxMOskvh37hxIUT3NfvPqtfw9/Nnz9n/Mm3133LxK4TrX5+IYQFygq2ivRCVWb4z87GjhYuLYoFW4ZhEJMSIz1bNUSyXYVooNp4tCElK4V5G+fR2r0113S+pkau42zvzI3dbqyRcwshLODmppcJKjEj0dQL5d3Eu9JJ7SULm55LP0dWbpYEWzVEeraEaKBM5R8iYiO4p+89MlNQiMYsMLBUz1Yzp2Y42jpWKl/LxFTI2DAMlhxYwoCFetHo7i26W6W5ojgJtoRooEzlH5rYN+HWnrfWcWuEEDUqKAj27i02I1EpRUuXllXqjfJz9ePY+WMM+WwI1/94Pfa29iy/cTkj2o+wZqtFvmoFW0opT6XUWqVUZP5jszKOa62UWqOUOqCU2q+Ualud6wohoK1HWxSK6T2m08zZ7H89IURjccstkJioq9QX8dIVL/HIoEfAMPQxP/9s0ekC3AJIzkrmyLkjLBi3gF137mJsx7E10HABoAzDqPqTlXoFOGcYxktKqceAZoZhPGrmuA3AfMMw1iqlXIA8wzDSKjp/WFiYsX379iq3T4jG7vdjv9PPvx+ujq513RQhRE17+mn473/hm2/gppuK7zt6VA81Dh8O69YVbjcMPfxoKh+RLy41jl8P/cqUkCm4OLhUvi3btsH330NODsTEwDXXwNTylwW7FCilwg3DCCu1vZrB1iFgmGEYMUopX2CDYRidShzTFVhgGMbgyp5fgi0hhBAiX04ODBsGu3frhalNsxQBPvwQ7roL7O3h3DlwcYGMDJg1C776CtasgZEjrdeWa6+FZct0sdesLAgNhS1brHf+BqqsYKu6OVstDMOIyf8+Fmhh5piOwAWl1BKl1E6l1KtKKdtyGjpLKbVdKbU9Pj6+ms0TQgghGgk7O/j2W/14ww06yDFZuxZsbSE7G9av171Nw4bpQAusHwhFR+uli5KSdFtOn7bu+RuZCoMtpdTvSqm9Zr6KzTM3dBeZuW4yO2AI8BDQB2gPzCjreoZhLDAMI8wwjDAfH5/KvBYhhBCicWvdGj79FMLD4fHH9bbcXPjjD7jxRmjSBN59F/r0gT174KefoGNHiIiwbjtiYsA3PzG/VSv9c06Oda/RiFQ4V9wwjDJX3VRKnVVK+RYZRowzc9gZIMIwjGP5z/kZ6A8srFqThRBCiEvYhAkweza8/jrMnKlnKF64AGPH6sfly3VQtnkz9OgBP/wA1kzJMQyIjQW//JITAQGQl6e3BQRY7zqNSHWHEX8Bpud/Px1YZuaYbYCHUsrUTTUc2F/N6wohhBCXrlvzy70cOqST1QEGD4YHH4T//Edv69FDb+/RA44dg4sXrXPtxEQ9XGnq2TIFWDKUWKbqBlsvASOVUpHAFfk/o5QKU0p9AmAYRi56CHGdUmoPoICPq3ldIYQQ4tJlCnRiYiAqSudr+fnpPK0vvtAV501CQ/Xj7t3WuXZ0dPE2tGqlH8+csc75G6FqlZw2DCMRKFUBzTCM7cBtRX5eC0hZWiGEEMIafHzAxkYHW9HROvCxKaP/xNTDtWuX7v2qrpj8eXEle7Yk2CqTVJAXQgghGhpbW2jRojDY8itnyR4/P/D2tl6SvCnYMl3Tw0Mn5sswYpkk2BJCCCEaIl/fwmDL37/s45SCvn11sdNq1NYsULJnSyk9lCg9W2WSYEsIIYRoiIoGW+X1bIGuhXX8uJ6hWF3R0eDuDs7OhdsCAiTYKocEW0IIIURD5OurA6jz5ysOtq69Vg/1ff119a9btMaWSatWMoxYjmolyAshhBCijvj66gruUHGw5eKi63P98AO8+SY4Opo/bssW+Ocf6NcPHBx0lXpXV+jWrfCYmJjS1wsIKCxsaiehRUnSsyWEEEI0REUDnoqCLdD1t86fh8WLyz7mySfhgQdg0CBdhX7QIOjeXS/Ns3WrPsZcz1ZAgK5k/++/lX8dlwAJtoQQQoiGqGjAU16CvMnIkdC5s648X1aifHS0Pm7ZMvjlF1i9Gv73P102on9/PRxpKjVR1KhRenbkZZfBc88VX7dRSLAlhBBCNEhFAx5LerZsbOC++2DHDti0yfwxsbHQqROMHw9XX62DqAce0BXo583TazBmZpa+Xtu2sG8fTJkCzz6rZz9aez3GBkyCLSGEEKIhMgVbTk661pUlbr4Z3Nzgm29K70tP1zlgJXutQOdtPf20Drree08PSZbk5aUT8H/+Gc6e1cOQq1db+moaNQm2hBBCiIaoRQv96Oena11ZokkTCAqCU6dK7ytZP8scLy+4+279WJZrrtG9XB4e8N13hdtnz4bp08t8WmMmUwaEEEKIhsjBQVeGt2QIsSg/Pzh5svR2S4ItS3l6wsCBenYj6ByxRYt0sHcJkp4tIYQQoqHq1Qt6967cc/z9CxeTLio2Vj+2bFn9dgEMGACRkZCQAEeOQHy8XjQ7L886529ApGdLCCGEaKiqkhPl56cDoMzM4vW2rNmzBTrYAl23KyFBf5+To/O5rHWNBkJ6toQQQoiGSinL87VMTGUiTMGVSUyMXuDax8c6bevTR59vy5biywRdgpXmJdgSQgghLiWmHK+SQ4kxMTrp3sZKoUGTJhAaChs2wF9/FQZ5EmwJIYQQolEzBVtRUcW3x8ZaL1/L5Oqrda/WgQMwebLeJsGWEEIIIRo1Uw+TuZ4ta+dSPf00LFkCkybBnDng7Axnzlj3Gg2AJMgLIYQQlxJPT102wlywFRZm3WvZ2Oglfq69Vv8cECA9W0IIIYRo5JTSQ4lFhxFzciAuruZnCbZqJcGWEEIIIS4BJWttbdmiC49aO2erJAm2hBBCCHFJ8PPTwdapU3q9xKFD9RI8I0fW7HVbtdLXzcmp2evUMxJsCSGEEJcaPz84ehQ6dtTL6Dz2mP45KKhmr9uqla4gb6pWf4mQYEsIIYS41AQH696lyZPh8GF48UVwd6/567Zvrx9NayZeIpRhGHXdhjKFhYUZ27dvr+tmCCGEEI1Lbi6cP68Xsq5NOTk60LO3h127dIX5RkQpFW4YRqkpndKzJYQQQlxqbG1rP9ACsLOD55+Hffvgu+9q//p1RIItIYQQQtSeiRP1Mj7PPAPZ2XXdmlohwZYQQgghao+NDcyfD8eOwaef1nVraoUEW0IIIYSoXWPGwKBBMG8epKfXdWtqnARbQgghhKhdSsELL+iaW++/X9etqXESbAkhhBCi9g0dCqNG6bITFy/WdWtqVLWDLaWUp1JqrVIqMv+xWRnHvaKU2qeUOqCUelsppap7bSGEEEI0YPPnQ2IifPBBXbekRlmjZ+sxYJ1hGEHAuvyfi1FKDQQGAd2BEKAPcJkVri2EEEKIhqp3b+jTB375pa5bUqOsEWxdA3yR//0XwAQzxxiAE+AAOAL2wFkrXFsIIYQQDdmoUfDPP7rIaiNljWCrhWEYMfnfxwItSh5gGMYWYD0Qk//1m2EYB6xwbSGEEEI0ZKNH6/US162r65bUGIuCLaXU70qpvWa+ril6nKHX/im1/o9SKhDoAgQA/sBwpdSQMq41Sym1XSm1PT4+vtIvSAghhBANSL9+el3GN9+EHj3g77/rukVWZ2fJQYZhXFHWPqXUWaWUr2EYMUopXyDOzGHXAv8YhpGS/5xVwABgk5lrLQAWgF4b0ZL2CSGEEKKBsrODESNgyRL988qVugZXI2KNYcRfgOn5308Hlpk55hRwmVLKTillj06Ol2FEIYQQQsDTT8Ozz0LbtnD4cF23xuos6tmqwEvAj0qpW4GTwGQApVQYcKdhGLcBi4HhwB70MONqwzB+tcK1hRBCCNHQhYbqr23b4NChum6N1VU72DIMIxEYYWb7duC2/O9zgTuqey0hhBBCNGKdOulE+bw8vYZiI9F4XokQQgghGrZOnSAjA06fruuWWJUEW0IIIYSoHzp21I+NLG9Lgi0hhBBC1A+dOunHRpa3JcGWEEIIIeqHli3B1VWCLSGEEEKIGqGUHkrcuRPS0+u6NVYjwZYQQggh6o++fXUVeX//RpO7JcGWEEIIIeqPt9/WVeTPn4dFi+q6NVYhwZYQQggh6g87OxgzRq+T2EgWp5ZgSwghhBD1z4gRsHlzo8jdkmBLCCGEEPXPiBGQmakDrgZOgi0hhBBC1D9DhughxUYwlCjBlhBCCCHqH1dXPTPxjz/quiXVJsGWEEIIIeqn4cNh2zZISqrrllSLBFtCCCGEqJ9GjIC8PPjzz7puSbVIsCWEEEKI+mnAAHByavBDiRJsCSGEEKJ+cnSEwYMbfJK8BFtCCCGEqL9GjIC9e+Hs2bpuSZVJsCWEEEKI+mv4cP24fn3dtqMaJNgSQgghRP3Vuze4uzfooUQJtoQQQghRf9nawrBhEmwJIYQQQtSY4cPh+HH91QBJsCWEEEKI+m3ECP34zTcNcmFqCbaEEEIIUb917Qpt28LTT0P79pCTU9ctqhQJtoQQQghRvykFO3fC/fdDbCwkJtZ1iypFgi0hhBBC1H8eHtC/v/4+Pr5Om1JZEmwJIYQQomHw9taPCQl1245KkmBLCCGEEA2DBFtCCCGEEDVIgi0hhBBCiBrk5aUfJdgSQgghhKgBjo7g6nppBVtKqUlKqX1KqTylVFg5x41WSh1SSh1RSj1WnWsKIYQQ4hLm43NpBVvAXuA6YGNZByilbIH3gDFAV+BGpVTXal5XCCGEEJcib+9LK9gyDOOAYRiHKjisL3DEMIxjhmFkAd8D11TnukIIIYS4RF1qwZaF/IHTRX4+k79NCCGEEKJyGmCwZVfRAUqp34GWZnY9aRjGMms3SCk1C5gF0Lp1a2ufXgghhBANWWMMtgzDuKKa14gCWhX5OSB/W1nXWwAsAAgLCzOqeW0hhBBCNCbe3pCaCunp4Oxc162xSG0MI24DgpRS7ZRSDsANwC+1cF0hhBBCNDamwqYNaDHq6pZ+uFYpdQYYAKxQSv2Wv91PKbUSwDCMHGAO8BtwAPjRMIx91Wu2EEIIIS5JDbCKfIXDiOUxDGMpsNTM9mjgqiI/rwRWVudaQgghhBANMdiSCvJCCCGEaDgk2BJCCCGEqEGmYCs+vm7bUQkSbAkhhBCi4fDyAl9fWL26rltiMQm2hBBCCNFw2NjA7bfDqlVw/Hhdt8YiEmwJIYQQomG5/XYddH30UcXHxsTAP//UfJvKIcGWEEIIIRqWgAC46ir4/vvyjzMMuOsuuOIKOHeudtpmhgRbQgghhGh4OnaEuLjyj/nxR1i2DJ59Fjw9a6VZ5kiwJYQQQoiGx8NDL9mTlWV+v2HAffdBnz5w//212bJSJNgSQgghRMPj7q4fk5LM7794EWJjYcoUsLWtvXaZIcGWEEIIIRqeioKt2Fj92LJl7bSnHBJsCSGEEKLh8fDQjxcumN8vwZYQQgghRDVIz5YQQgghRA0y9WxJsCWEEEIIUQNMPVvlDSPa20OzZrXWpLJIsCWEEEKIhseSYcQWLXSl+TpW9y0QQgghhKgsNzf9WF7PVosWtdac8kiwJYQQQoiGx9YWXF3L79mqB/laIMGWEEIIIRoqDw8JtoQQQgghaoy7u/lhxNxcvW6iBFtCCCGEENXg7m6+ZyshAfLyJNgSQgghhKgWDw/zPVv1qMYWSLAlhBBCiIaqrJ4tCbaEEEIIIaygrAT548f1owRbQgghhBDVYEqQN4zCbfv2weOPQ5cu0KZNnTWtKAm2hBBCCNEwubvrmYdpafrn06dh9GhwdoZVq/RyPfWAXV03QAghhBCiSoouRp2VBWPGwMWLsHFjvenVAunZEkIIIURDZVofMTYWJkyAw4dh6VLo0aNOm1WS9GwJIYQQomEy9Wz95z86V+u772D48DptkjnSsyWEEEKIhsnUs7VvH7z+OtxwQ922pwwSbAkhhBCiYQoI0I8PPgj331+3bSmHDCMKIYQQomFq1Qqio+tNPa2yVKtnSyk1SSm1TymVp5QKK+OYVkqp9Uqp/fnH3ludawohhBBCFPD1BaXquhXlqu4w4l7gOmBjOcfkAA8ahtEV6A/MVkp1reZ1hRBCCCEahGoNIxqGcQBAlRNRGoYRA8Tkf5+slDoA+AP7q3NtIYQQQoiGoFYT5JVSbYGewNbavK4QQgghRF2psGdLKfU7YC7z7EnDMJZZeiGllAvwE3CfYRgXyzluFjALoHXr1paeXgghhBCiXqow2DIM44rqXkQpZY8OtL4xDGNJBddbACwACAsLM8o7VgghhBCivqvxYUSlE7oWAgcMw3i9pq8nhBBCCFGfVLf0w7VKqTPAAGCFUuq3/O1+SqmV+YcNAm4GhiulIvK/rqpWq4UQQgghGojqzkZcCiw1sz0auCr/+7+A+l0AQwghhBCihshyPUIIIYQQNUiCLSGEEEKIGqQMo/5O+FNKxQMnK/EUbyChhppzqZJ7WnPk3tYsub81T+5xzZL7W7Nq4v62MQzDp+TGeh1sVZZSarthGGbXaBRVI/e05si9rVlyf2ue3OOaJfe3ZtXm/ZVhRCGEEEKIGiTBlhBCCCFEDWpswdaCum5AIyT3tObIva1Zcn9rntzjmiX3t2bV2v1tVDlbQgghhBD1TWPr2RJCCCGEqFfqNNhSSrVSSq1XSu1XSu1TSt2bv91TKbVWKRWZ/9gsf/tUpdRupdQepdRmpVSP8s5TxjVHK6UOKaWOKKUeK7J9Tv42QynlXdOvvabUs3u6UCm1K//8i5VSLjX9+mtSPbu3nyuljhdZAiu0hl9+jatn93dTkXsbrZT6uYZffq2oZ/d4uFJqh1Jqr1LqC6VUtVY0qQ/q6P5+qpSKU0rtLbF9Uv5z85RSjWJGoxXvr5NS6l+l/z7tU0o9V841p+efN1IpNb3I9vlKqdNKqRSLGm8YRp19Ab5Ar/zvXYHDQFfgFeCx/O2PAS/nfz8QaJb//Rhga3nnMXM9W+Ao0B5wAHaZjgN6Am2BE4B3Xd6XRnRP3Yoc97rp+g31q57d28+BiXV9Txrr/S1x3E/Af+r6/jSme4z+oH8a6Jh/3Dzg1rq+Pw3t/ubvHwr0AvaW2N4F6ARsAMLq+t7Us/urAJf87+2BrUB/M9fzBI7lPzbL/950vv757UmxqO11ffNKvLBlwEjgEOBb5OYeMnNsMyCqvPOY2T4A+K3Iz48Dj5c45gQNONiqp/dUAR8Aj9b1/Wgs95ZGGGzVp/tbZJsbcJ4iHxwa01dd3WPABzhaZPsQYGVd34+Gdn+L7G9LiWCryL4NNJJgqybuL9AE2AH0M7PvRuCjIj9/BNxY4hiLgq16k7OllGqL7l3aCrQwDCMmf1cs0MLMU24FVlVwnpL80Z+mTM7kb2uU6sM9VUp9ln+9zsA7lX0N9VV9uLfA/Pwu8jeUUo6VfQ31WT25vwATgHWGYVy0vPUNQx3f4wTArsjw1kSgVaVfRD1WS/f3klXd+6uUslVKRQBxwFrDMGo0ZqgXwZbSuTw/AfeVfFMzdOholDj+cvSNe9TS81xq6ss9NQzjFsAPOABMqezz66N6cm8fRwewfdBd3I+Wf3jDUU/ur8mNwHdVfG69Vdf3OP8aNwBvKKX+BZKB3Cq8lHqpru9vY2eN+2sYRq5hGKFAANBXKRVSk22u82BLKWWPvmnfGIaxJH/zWaWUb/5+X3TkaTq+O/AJcI1hGInlnSc/mc6U5HonEEXxT08B+dsalfp2Tw3DyAW+B6637iutffXl3hqGEWNomcBnQN+aecW1q77c3/zjvdH3dYX1X2ndqS/32DCMLYZhDDEMoy+wEZ1/0+DV8v295Fjr/poYhnEBWA+MVkr1K3J/x2PNmKGmxlIt+ULn8nwJvFli+6sUT3Z7Jf/71sARYKAl5zFzPTt0gls7CpM1g0scc4IGnLNVX+5p/vMDi5zrNeC1ur4/jeHe5u/zLXKuN4GX6vr+NKb7m7//TuCLur4vjfUeA83zHx2BdcDwur4/De3+Fjm+LZdAzpYV768P4JH/vTOwCRhn5nqewHF0vlez/O89SxxT/xPkgcHo7r7dQET+11WAV/5/vkjgd9OLQ0en54scu72885RxzavQn6COAk8W2T4XPR6bA0QDn9T1L1ZDvqfoXtO/gT3AXuAbGniScX25t/nb/yhyb78mf2ZNQ/6qT/c3f98GYHRd35fGeo/RfyAPoJOb76vre9OA7+93QAyQjf4bdmv+9mvzf84EzlJkokJD/bLi/e0O7Mw/z17g/8q55kx0wHYEuKXI9lfy729e/uOz5bVdKsgLIYQQQtSgOs/ZEkIIIYRozCTYEkIIIYSoQRJsCSGEEELUIAm2hBBCCCFqkARbQgghhBA1SIItIYQQQogaJMGWEEIIIUQNkmBLCCGEEKIG/T+6CwyLzWTe/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(trade_df['Cumulative Market Returns'], color='r', label='Market Returns')\n",
    "plt.plot(trade_df['Cumulative Strategy Returns'], color='g', label='Strategy Returns')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "olfypJ520h0k"
   },
   "source": [
    "## Showcase 2 - Support Vector Machines for regime/trend prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let me begin by explaining the agenda here:\n",
    "\n",
    "1. Create an unsupervised ML ( machine learning) algorithm to predict the regimes.\n",
    "2. Plot these regimes to visualize them.\n",
    "3. Train a Support Vector Classifier algorithm with the regime as one of the features.\n",
    "4. Use this Support Vector Classifier algorithm to predict the current day’s trend at the Opening of the market.\n",
    "5. Visualize the performance of this strategy on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas_datareader import data as pdr\n",
    "import seaborn as sns \n",
    "import matplotlib.pyplot as plt\n",
    "import talib as ta\n",
    "from sklearn import mixture as mix\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "import yfinance as yf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>148.25000</td>\n",
       "      <td>148.25000</td>\n",
       "      <td>143.875000</td>\n",
       "      <td>145.4375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>143.53125</td>\n",
       "      <td>144.06250</td>\n",
       "      <td>139.640625</td>\n",
       "      <td>139.7500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>139.93750</td>\n",
       "      <td>141.53125</td>\n",
       "      <td>137.250000</td>\n",
       "      <td>140.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>139.62500</td>\n",
       "      <td>141.50000</td>\n",
       "      <td>137.750000</td>\n",
       "      <td>137.7500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>140.31250</td>\n",
       "      <td>145.75000</td>\n",
       "      <td>140.062500</td>\n",
       "      <td>145.7500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High         Low     Close\n",
       "Date                                                  \n",
       "2000-01-03  148.25000  148.25000  143.875000  145.4375\n",
       "2000-01-04  143.53125  144.06250  139.640625  139.7500\n",
       "2000-01-05  139.93750  141.53125  137.250000  140.0000\n",
       "2000-01-06  139.62500  141.50000  137.750000  137.7500\n",
       "2000-01-07  140.31250  145.75000  140.062500  145.7500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the data from Yahoo\n",
    "df= pdr.get_data_yahoo('SPY', '2000-01-01', '2012-01-01')\n",
    "\n",
    "df = df.dropna()\n",
    "df = df[['Open', 'High', 'Low','Close']]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10  # look back period of 10 days\n",
    "t = 0.8 # 80% data for training and remaining 20% data for testing\n",
    "split =int(t*len(df))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's shift the High, Low and Close columns by 1, to access only the past data. After this, let's created various technical indicators such as, RSI, SMA, ADX, Correlation, Parabolic SAR, and the Return of the past 1- day on an Open to Open basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Open       High         Low     Close       high         low  \\\n",
      "Date                                                                            \n",
      "2000-01-03  148.25000  148.25000  143.875000  145.4375        NaN         NaN   \n",
      "2000-01-04  143.53125  144.06250  139.640625  139.7500  148.25000  143.875000   \n",
      "2000-01-05  139.93750  141.53125  137.250000  140.0000  144.06250  139.640625   \n",
      "2000-01-06  139.62500  141.50000  137.750000  137.7500  141.53125  137.250000   \n",
      "2000-01-07  140.31250  145.75000  140.062500  145.7500  141.50000  137.750000   \n",
      "\n",
      "               close  RSI  SMA  Corr         SAR  ADX    Return  \n",
      "Date                                                             \n",
      "2000-01-03       NaN  NaN  NaN   NaN         NaN  NaN       NaN  \n",
      "2000-01-04  145.4375  NaN  NaN   NaN         NaN  NaN -0.032347  \n",
      "2000-01-05  139.7500  NaN  NaN   NaN  148.250000  NaN -0.025357  \n",
      "2000-01-06  140.0000  NaN  NaN   NaN  146.528125  NaN -0.002236  \n",
      "2000-01-07  137.7500  NaN  NaN   NaN  144.672500  NaN  0.004912  \n"
     ]
    }
   ],
   "source": [
    "df['high']=df['High'].shift(1)\n",
    "df['low']=df['Low'].shift(1)\n",
    "df['close']=df['Close'].shift(1)\n",
    "df['RSI']=ta.RSI(np.array(df['close']), timeperiod=n)\n",
    "df['SMA']= df['close'].rolling(window=n).mean()\n",
    "df['Corr']= df['SMA'].rolling(window=n).corr(df['close'])\n",
    "df['SAR']=ta.SAR(np.array(df['high']),np.array(df['low']),\\\n",
    "                  0.2,0.2)\n",
    "df['ADX']=ta.ADX(np.array(df['high']),np.array(df['low']),\\\n",
    "                  np.array(df['close']), timeperiod =n)\n",
    "df['Corr'][df.Corr>1]=1\n",
    "df['Corr'][df.Corr<-1]=-1 \n",
    "df['Return']= np.log(df['Open']/df['Open'].shift(1))\n",
    "\n",
    "print(df.head())\n",
    "\n",
    "df=df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 621.5x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean for regime 0:  -0.01354361468026196\n",
      "Co-Variance for regime 0:  0.34228226342462287\n",
      "Mean for regime 1:  -1.3584140837627232\n",
      "Co-Variance for regime 1:  0.37004225826594567\n",
      "Mean for regime 2:  1.1515138267969611\n",
      "Co-Variance for regime 2:  0.39132398659487155\n",
      "Mean for regime 3:  -0.801900436799713\n",
      "Co-Variance for regime 3:  1.1814840292494673\n",
      "        Date  Regime        Open        high         low       close  \\\n",
      "0 2009-09-09       1  103.120003  103.050003  102.389999  102.940002   \n",
      "1 2009-09-10       1  103.800003  104.080002  102.800003  103.730003   \n",
      "2 2009-09-11       1  104.989998  104.860001  103.220001  104.790001   \n",
      "3 2009-09-14       1  103.879997  105.300003  104.279999  104.769997   \n",
      "4 2009-09-15       1  105.449997  105.459999  103.150002  105.279999   \n",
      "\n",
      "         RSI      SMA      Corr         SAR        ADX    Return  \\\n",
      "0  61.016205  102.124 -0.712279   99.570000  27.067911  0.001164   \n",
      "1  64.627979  102.181 -0.591800  100.266000  27.615840  0.006573   \n",
      "2  68.920785  102.343 -0.312803  101.028801  28.737307  0.011399   \n",
      "3  68.745839  102.480  0.069446  101.795041  30.084067 -0.010629   \n",
      "4  70.842418  102.670  0.572570  102.496033  29.362099  0.015001   \n",
      "\n",
      "   market_cu_return  \n",
      "0          0.001164  \n",
      "1          0.007737  \n",
      "2          0.019136  \n",
      "3          0.008507  \n",
      "4          0.023508  \n"
     ]
    }
   ],
   "source": [
    "# created an unsupervised learning algorithm to make the regime prediction\n",
    "\n",
    "ss= StandardScaler()\n",
    "unsup = mix.GaussianMixture(n_components=4, \n",
    "                            covariance_type=\"spherical\", \n",
    "                            n_init=100, \n",
    "                            random_state=42)\n",
    "df=df.drop(['High','Low','Close'],axis=1)\n",
    "unsup.fit(np.reshape(ss.fit_transform(df[:split]),(-1,df.shape[1])))\n",
    "regime = unsup.predict(np.reshape(ss.transform(df[split:]),\\\n",
    "                                                   (-1,df.shape[1])))\n",
    "\n",
    "Regimes=pd.DataFrame(regime,columns=['Regime'],index=df[split:].index)\\\n",
    "                     .join(df[split:], how='inner')\\\n",
    "                          .assign(market_cu_return=df[split:]\\\n",
    "                                  .Return.cumsum())\\\n",
    "                                  .reset_index(drop=False)\\\n",
    "                                  .rename(columns={'index':'Date'})\n",
    "\n",
    "order=[0,1,2,3]\n",
    "fig = sns.FacetGrid(data=Regimes,hue='Regime',hue_order=order,aspect=2,height= 4)\n",
    "fig.map(plt.scatter,'Date','market_cu_return', s=4).add_legend()\n",
    "plt.show()\n",
    "\n",
    "for i in order:\n",
    "    print('Mean for regime %i: '%i,unsup.means_[i][0])\n",
    "    print('Co-Variance for regime %i: '%i,(unsup.covariances_[i]))\n",
    "\n",
    "print(Regimes.head())\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above code, we created an unsupervised-algo that will divide the market into 4 regimes, based on the criterion of its own choosing. We have not provided any train dataset with labels. Next, we will fit the data and predict the regimes. Then we will be storing these regime predictions in a new variable called regime.\n",
    "\n",
    "This graph looks pretty good. Without actually looking at the factors based on which the classification was done, we can conclude a few things just by looking at the chart.\n",
    "\n",
    "- The # zone is the low volatility or the sideways zone\n",
    "- The # zone is high volatility zone or panic zone.\n",
    "- The # zone is a breakout zone.\n",
    "- The # zone: Not entirely sure but let us find out.\n",
    "\n",
    "The data can be inferred as follows:\n",
    "\n",
    "- Regime 0: Low mean and High covariance.\n",
    "- Regime 1: High mean and High covariance.\n",
    "- Regime 2: High mean and Low covariance.\n",
    "- Regime 3: Low mean and Low covariance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We scale the Regimes data frame, excluding the Date and Regimes columns, created in the earlier piece of code and saved it back in the same columns. By doing so, we will not be losing any features but the data will be scaled and ready for training the support vector classifier algorithm. Next, we create a signal column which would act as the prediction values. The algorithm would train on the features’ set to predict this signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ss1 =StandardScaler()\n",
    "columns =Regimes.columns.drop(['Regime','Date'])    \n",
    "Regimes[columns]= ss1.fit_transform(Regimes[columns])\n",
    "Regimes['Signal']=0\n",
    "Regimes.loc[Regimes['Return']>0,'Signal']=1\n",
    "Regimes.loc[Regimes['Return']<0,'Signal']=-1\n",
    "Regimes['return'] = Regimes['Return'].shift(1)\n",
    "Regimes=Regimes.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Date\n",
      "2011-07-18    1\n",
      "2011-07-19    1\n",
      "2011-07-20    1\n",
      "2011-07-21    1\n",
      "2011-07-22    1\n",
      "             ..\n",
      "2011-12-23    1\n",
      "2011-12-27    1\n",
      "2011-12-28    1\n",
      "2011-12-29    1\n",
      "2011-12-30    1\n",
      "Name: Pred_Signal, Length: 117, dtype: int64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# SVM Classifier       \n",
    "cls= SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
    "    decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',\n",
    "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
    "    tol=0.001, verbose=False)\n",
    "\n",
    "split2= int(.8*len(Regimes))\n",
    "\n",
    "X = Regimes.drop(['Signal','Return','market_cu_return','Date'], axis=1)\n",
    "y= Regimes['Signal']\n",
    "\n",
    "cls.fit(X[:split2],y[:split2])\n",
    "\n",
    "p_data=len(X)-split2\n",
    "\n",
    "df['Pred_Signal']=0\n",
    "df.iloc[-p_data:,df.columns.get_loc('Pred_Signal')]=cls.predict(X[split2:])\n",
    "\n",
    "print(df['Pred_Signal'][-p_data:])\n",
    "\n",
    "df['str_ret'] =df['Pred_Signal']*df['Return'].shift(-1)\n",
    "\n",
    "df['strategy_cu_return']=0.\n",
    "df['market_cu_return']=0.\n",
    "df.iloc[-p_data:,df.columns.get_loc('strategy_cu_return')] \\\n",
    "       = np.nancumsum(df['str_ret'][-p_data:])\n",
    "df.iloc[-p_data:,df.columns.get_loc('market_cu_return')] \\\n",
    "       = np.nancumsum(df['Return'][-p_data:])\n",
    "Sharpe = (df['strategy_cu_return'][-1]-df['market_cu_return'][-1])\\\n",
    "           /np.nanstd(df['strategy_cu_return'][-p_data:])\n",
    "\n",
    "plt.plot(df['strategy_cu_return'][-p_data:],color='g',label='Strategy Returns')\n",
    "plt.plot(df['market_cu_return'][-p_data:],color='r',label='Market Returns')\n",
    "plt.figtext(0.14,0.9,s='Sharpe ratio: %.2f'%Sharpe)\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showcase 3 - Create trading strategy using KNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.metrics import accuracy_score\n",
    "from pandas_datareader import data as pdr\n",
    "import yfinance as yf\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "register_matplotlib_converters()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03</th>\n",
       "      <td>127.760002</td>\n",
       "      <td>128.380005</td>\n",
       "      <td>127.430000</td>\n",
       "      <td>127.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04</th>\n",
       "      <td>127.199997</td>\n",
       "      <td>127.809998</td>\n",
       "      <td>126.709999</td>\n",
       "      <td>127.699997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05</th>\n",
       "      <td>127.010002</td>\n",
       "      <td>128.229996</td>\n",
       "      <td>126.430000</td>\n",
       "      <td>128.039993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06</th>\n",
       "      <td>128.199997</td>\n",
       "      <td>128.220001</td>\n",
       "      <td>127.290001</td>\n",
       "      <td>127.709999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09</th>\n",
       "      <td>128.000000</td>\n",
       "      <td>128.179993</td>\n",
       "      <td>127.410004</td>\n",
       "      <td>128.020004</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Open        High         Low       Close\n",
       "Date                                                      \n",
       "2012-01-03  127.760002  128.380005  127.430000  127.500000\n",
       "2012-01-04  127.199997  127.809998  126.709999  127.699997\n",
       "2012-01-05  127.010002  128.229996  126.430000  128.039993\n",
       "2012-01-06  128.199997  128.220001  127.290001  127.709999\n",
       "2012-01-09  128.000000  128.179993  127.410004  128.020004"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the data from Yahoo\n",
    "df= pdr.get_data_yahoo('SPY', '2012-01-01', '2021-01-01')\n",
    "\n",
    "df = df.dropna()\n",
    "df = df[['Open', 'High', 'Low','Close']]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open-Close</th>\n",
       "      <th>High-Low</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-01-03</th>\n",
       "      <td>0.260002</td>\n",
       "      <td>0.950005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-04</th>\n",
       "      <td>-0.500000</td>\n",
       "      <td>1.099998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-05</th>\n",
       "      <td>-1.029991</td>\n",
       "      <td>1.799995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-06</th>\n",
       "      <td>0.489998</td>\n",
       "      <td>0.930000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-09</th>\n",
       "      <td>-0.020004</td>\n",
       "      <td>0.769989</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Open-Close  High-Low\n",
       "Date                            \n",
       "2012-01-03    0.260002  0.950005\n",
       "2012-01-04   -0.500000  1.099998\n",
       "2012-01-05   -1.029991  1.799995\n",
       "2012-01-06    0.489998  0.930000\n",
       "2012-01-09   -0.020004  0.769989"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predictor variables\n",
    "df['Open-Close']= df.Open -df.Close\n",
    "df['High-Low']  = df.High - df.Low\n",
    "df =df.dropna()\n",
    "X= df[['Open-Close', 'High-Low']]\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Target variable\n",
    "Y= np.where(df['Close'].shift(-1)>df['Close'],1,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Splitting the dataset\n",
    "split_percentage = 0.7\n",
    "split = int(split_percentage*len(df))\n",
    "\n",
    "X_train = X[:split]\n",
    "Y_train = Y[:split]\n",
    "\n",
    "X_test = X[split:]\n",
    "Y_test = Y[split:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train_data Accuracy: 0.61\n",
      "Test_data Accuracy: 0.56\n"
     ]
    }
   ],
   "source": [
    "# Instantiate KNN learning model(k=15)\n",
    "knn = KNeighborsClassifier(n_neighbors=15)\n",
    "\n",
    "# fit the model\n",
    "knn.fit(X_train, Y_train)\n",
    "\n",
    "# Accuracy Score\n",
    "accuracy_train = accuracy_score(Y_train, knn.predict(X_train))\n",
    "accuracy_test = accuracy_score(Y_test, knn.predict(X_test))\n",
    "\n",
    "print ('Train_data Accuracy: %.2f' %accuracy_train)\n",
    "print ('Test_data Accuracy: %.2f' %accuracy_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Predicted Signal\n",
    "df['Predicted_Signal'] = knn.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SPY Cumulative Returns\n",
    "df['SPY_returns'] = np.log(df['Close']/df['Close'].shift(1))\n",
    "Cumulative_SPY_returns = df[split:]['SPY_returns'].cumsum()*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cumulative Strategy Returns \n",
    "df['Startegy_returns'] = df['SPY_returns']* df['Predicted_Signal'].shift(1)\n",
    "Cumulative_Strategy_returns = df[split:]['Startegy_returns'].cumsum()*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results to visualize the performance\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(Cumulative_SPY_returns, color='r',label = 'SPY Returns')\n",
    "plt.plot(Cumulative_Strategy_returns, color='g', label = 'Strategy Returns')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sharpe ratio: 0.66\n"
     ]
    }
   ],
   "source": [
    "# Calculate Sharpe reatio\n",
    "Std = Cumulative_Strategy_returns.std()\n",
    "Sharpe = (Cumulative_Strategy_returns-Cumulative_SPY_returns)/Std\n",
    "Sharpe = Sharpe.mean()\n",
    "print('Sharpe ratio: %.2f'%Sharpe )"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "1_ML_Intro.ipynb",
   "provenance": [
    {
     "file_id": "1MlepN6Hfgtvpddw6b8WIC_UWGvFkWlYT",
     "timestamp": 1547849262566
    }
   ],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}