511-exercises.Rmd

---
title: "Forecasting: Principles and Practice Chapter 5 Exercises"
author: "Neil Martin"
date: "2024-09-11"
output: html_document
---

```{r setup, include=FALSE}
load(".RData")
library(fpp3)
library(knitr)
library(ggplot2)
library(readxl)
library(dplyr)
library(readr)
library(seasonal)
library(latex2exp)
library(tsibble)
library(feasts)
library(tidyr)
```
#### Produce forecasts for the following series using whichever of NAIVE(y), SNAIVE(y) or RW(y ~ drift()) is more appropriate in each case:

#### Australian Population (global_economy)
#### Bricks (aus_production)
#### NSW Lambs (aus_livestock)
#### Household wealth (hh_budget).
#### Australian takeaway food turnover (aus_retail).

```{r model_benchmark}

global_economy |>
  filter(Country == "Australia") |>
  model(RW(Population ~ drift())) |>
  forecast(h = 5) |>
  autoplot(global_economy) +
  labs(title = "Australia Population",
       subtitle = "5 Year Population Forecast")

bricks <- aus_production |>
  filter_index("1970 Q1" ~ "2004 Q4") |>
  select(Bricks)

bricks

bricks |>
  model(SNAIVE(Bricks)) |>
  forecast(h = 5) |>
  autoplot(bricks) +
  labs(title = "Bricks",
       subtitle = "Future 5 Quarter Forecast")

aus_livestock |>
  filter(State == "New South Wales", Animal == 'Lambs') |>
  model(SNAIVE(Count)) |>
  forecast(h = 24) |>
  autoplot(aus_livestock) +
  labs(title = "Lambs in New South Wales",
       subtitle = "Dec 2018 - Dec 2020 Forecast")

hh_budget |>
  model(RW(Wealth ~ drift())) |>
  forecast(h = 5) |>
  autoplot(hh_budget) +
  labs(title = "Household Wealth",
       subtitle = "5 Year Household Wealth Forecast")

aus_retail |>
  filter(Industry == "Cafes, restaurants and takeaway food services") |>
  model(RW(Turnover ~ drift())) |>
  forecast( h = 24) |>
  autoplot(aus_retail) +
  labs(title = "Australian Takeaway Food Turnover",
       subtitle = "Apr 1982 - Dec 2018, Forecasted until Dec 2021") +
  facet_wrap(~State, scales = "free")

```   

#### Use the Facebook stock price (data set gafa_stock) to do the following:

#### Produce a time plot of the series.
#### Produce forecasts using the drift method and plot them.
#### Show that the forecasts are identical to extending the line drawn between the first and last observations.
#### Try using some of the other benchmark functions to forecast the same data set. Which do you think is best? Why?

```{r fb_stock_again}

fb_stock <- gafa_stock |>
  filter(Symbol == "FB") |>
  mutate(trading_day = row_number()) |>
  update_tsibble(index = trading_day, regular = TRUE)

fb_stock |> autoplot() +
    labs(title = "FB Stock Open Price")

fb_stock |>
  model(RW(Open ~ drift())) |>
  forecast(h = 63) |>
  autoplot(fb_stock) +
  labs(title = "FB Stock Open Price",
       y = "USD($)")

fb_stock |>
  model(RW(Open ~ drift())) |>
  forecast(h = 63) |>
  autoplot(fb_stock) +
  labs(title = "FB Stock Open Price") +
    geom_segment(aes(x = 1, y = 54.83, xend = 1258, yend = 134.45),
               colour = "red", linetype = "dashed")

fb_stock |>
  model(Drift = NAIVE(Open ~ drift()),
        Mean = MEAN(Open),
        Naive = NAIVE(Open)) |>
  forecast(h = 63) |>
  autoplot(fb_stock, level = NULL) +
  labs(title = "FB Stock Open Price",
       y = "USD($)")


```   

<p> None of the additional benchmarks are particularly useful. However, if I had to pick one it would be the drift.</p> 

#### Apply a seasonal naïve method to the quarterly Australian beer production data from 1992. Check if the residuals look like white noise, and plot the forecasts. The following code will help.

```{r whitenoise_beer}

# Extract data of interest
recent_production <- aus_production |>
  filter(year(Quarter) >= 1992)
# Define and estimate a model
fit <- recent_production |> model(SNAIVE(Beer))
# Look at the residuals
fit |> gg_tsresiduals()
# Look a some forecasts
fit |> forecast() |> autoplot(recent_production)

```   

<p> The residuals are not white noise. This can be concluded from the results from the ACF function demonstrating peaks in Q4. </p>

#### Repeat the previous exercise using the Australian Exports series from global_economy and the Bricks series from aus_production. Use whichever of NAIVE() or SNAIVE() is more appropriate in each case

```{r exports_bricks}

aus_exports <- global_economy |>
  filter(Country == "Australia")

aus_exports

fit <- aus_exports |>
  model(NAIVE(Exports))

fit |> gg_tsresiduals() +
  ggtitle("Residual Plot for Australian Exports")

fit |> forecast() |> autoplot(aus_exports) +
  ggtitle("Australian Exports")

fit <- bricks |>
  model(SNAIVE(Bricks))

fit |> gg_tsresiduals() +
  ggtitle("Residual Plot for Brick Production")

fit |> forecast() |> autoplot(bricks) +
  ggtitle("Australian Brick Production")
```   
<p> This data is not seasonal for the exports, therefore NAIVE is a better choice of model. For the Bricks data, the SNAIVE is better as this is broken down into quarters. The lag plot demonstrates clear seasonality with brick production increasing during Q4 and a reduction in production until the following quarter next year.</p>

#### Produce forecasts for the 7 Victorian series in aus_livestock using SNAIVE(). Plot the resulting forecasts including the historical data. Is this a reasonable benchmark for these series?

```{r 7_victorian_series}

aus_livestock |>
  filter(State == "Victoria") |>
  model(SNAIVE(Count ~ lag("2 years"))) |>
  forecast(h = "2 years") %>%
  autoplot(aus_livestock) +
  labs(title = "Animals in Victoria") +
  facet_wrap(~Animal, scales = "free")

```   

<p> Lambs and Calves may benefit from a trend model as overtime the number of calves has increased steadily and the number of lambs increased. For the rest, there is clear seasonal patterns within the data so a SNAIVE model is more suitable.</p>

#### Are the following statements true or false? Explain your answer.

#### Good forecast methods should have normally distributed residuals.

<p> Yes normally distributed residuals outlines that there is less of a chance of the data being white noise and the model being more accurate.</p>

#### A model with small residuals will give good forecasts.

<p> No, even though there is little difference between the forecast and the actual values, the pattern of the data might change.</p>

#### The best measure of forecast accuracy is MAPE.

<p> This is generally the most used metric.</p>

#### If your model doesn’t forecast well, you should make it more complicated.

<p> Nope, sometimes choosing a more simplistic model can provide better results.</p>

#### Always choose the model with the best forecast accuracy as measured on the test set.

<p> No, this can result in overfitting. Consider the metric the model has against the validation/testing set.</p>

#### For your retail time series (from Exercise 7 in Section 2.10):

#### Create a training dataset consisting of observations before 2011 using

```{r retail_split}

set.seed(12345678)
myseries <- aus_retail |>
  filter(`Series ID` == sample(aus_retail$`Series ID`,1))

myseries_train <- myseries |>
  filter(year(Month) < 2011)

```   

#### Check that your data have been split appropriately by producing the following plot.

```{r retail_split2}

autoplot(myseries, Turnover) +
  autolayer(myseries_train, Turnover, colour = "red")

``` 
#### Fit a seasonal naïve model using SNAIVE() applied to your training data (myseries_train).

```{r retail_split3}

fit <- myseries_train |>
  model(SNAIVE(Turnover))

``` 

#### Check the residuals.

```{r retail_split4}

fit |> gg_tsresiduals()

``` 
#### Produce forecasts for the test data

```{r retail_split5}

fc <- fit |>
  forecast(new_data = anti_join(myseries, myseries_train))
fc |> autoplot(myseries)

``` 

#### Compare the accuracy of your forecasts against the actual values.

```{r retail_split6}

fit |> accuracy()
fc |> accuracy(myseries)

```

#### Consider the number of pigs slaughtered in New South Wales (data set aus_livestock).

#### Produce some plots of the data in order to become familiar with it.

```{r q8}

pigs <- aus_livestock |>
  filter(Animal == "Pigs" & State == "New South Wales")

pigs

pigs |> autoplot()

pigs |> gg_season()

pigs |> gg_subseries()

```
#### Create a training set of 486 observations, withholding a test set of 72 observations (6 years).
```{r q81}

pigs_train <- pigs |>
  filter(year(Month) < 2014)

autoplot(pigs, Count) +
  autolayer(pigs_train, Count, colour = "red")

```

#### Try using various benchmark methods to forecast the training set and compare the results on the test set. Which method did best?

```{r q82}

pigs_fit <- pigs_train |>
  model(SNAIVE(Count))

accuracy(pigs_fit)

pigs_fc <- pigs_fit |>
  forecast(h = 12, level = NULL) |>
  autoplot(pigs_train) +
  labs(title = "Piggy Forecast")
pigs_fc

```
<p> Due to the stucture of the time series index, seasonal will likely always perform better. </p>

#### Check the residuals of your preferred method. Do they resemble white noise?

```{r q83}

pigs_fit |> gg_tsresiduals() +
  ggtitle("Residuals")

```

<p> No, there does not appear to be white noise as the residuals are consistent.

#### Create a training set for household wealth (hh_budget) by withholding the last four years as a test set.

```{r 91}

hh_budget_train <- hh_budget |>
  filter(Year <= 2010)

fit <- hh_budget_train |>
  model(RW(Wealth ~ drift()))

accuracy(fit)

fc <- fit |>
  forecast(h = 6, level=NULL) |>
  autoplot(hh_budget_train)+
  labs(title = "6 Year Household Wealth Forecast")

fc

```
#### Create a training set for Australian takeaway food turnover (aus_retail) by withholding the last four years as a test set.

```{r 101}

takeaway <- aus_retail |>
  filter(Industry == "Cafes, restaurants and takeaway food services")

tw_train <- takeaway |>
  filter(year(Month) <= 2014)

```
#### Fit all the appropriate benchmark methods to the training set and forecast the periods covered by the test set.

```{r q102} 

fit <- takeaway |>
  model(RW(Turnover ~ drift()))

fit

fit |>
  forecast ( h = 48) |>
  autoplot(takeaway) + 
  labs(title = "Australian Takeaway Food Turnover",
       subtitle = "Apr 1982 - Dec 2018, Forecasted until Dec 2022") +
  facet_wrap(~State, scales = "free")

```
#### We will use the Bricks data from aus_production (Australian quarterly clay brick production 1956–2005) for this exercise.

#### Use an STL decomposition to calculate the trend-cycle and seasonal indices. (Experiment with having fixed or changing seasonality.)

```{r q111} 

bricks_additive <- bricks |>
  model(classical_decomposition(Bricks, type = "additive")) |>
  components() |>
  autoplot() +
  labs(title = "Classical additive decomposition of Australian brick production")

bricks_additive


```

```{r q112} 

bricks_multi <- bricks |>
  model(classical_decomposition(Bricks, type = "multiplicative")) |>
  components() |>
  autoplot() +
  labs(title = "Classical multiplicative decomposition of Australian brick production")

bricks_multi


```

```{r q113} 

bricks_stl <- bricks |>
  model(STL(Bricks ~ season(window = 4), robust = TRUE)) |>
  components() |>
  autoplot() +
  labs(title = "STL decomposition of Australian brick production")

bricks_stl


bricks_stl_per <- bricks |>
  model(STL(Bricks ~ season(window = 'periodic'), robust = TRUE)) |>
  components() |>
  autoplot() +
  labs(title = "Periodic STL decomposition of Australian brick production")

bricks_stl_per


```

#### Compute and plot the seasonally adjusted data.


```{r q114} 

bricks

bricks_season <- bricks |>
  model(stl = STL(Bricks)) 

brick_comp <- components(bricks_season)

brick_season_adjust <- bricks |>
  autoplot(Bricks, color = "green") +
  autolayer(components(bricks_season), season_adjust, color = "red") +
  labs(title = "Seasonally adjusted Australian bricks data")

brick_season_adjust
```

#### Use a naïve method to produce forecasts of the seasonally adjusted data.

```{r q115} 

brick_trend <- brick_comp |>
  select(-c(.model, Bricks, trend, season_year, remainder))

brick_trend |>
  model(NAIVE(season_adjust)) |>
  forecast( h = "5 years") |>
  autoplot(brick_trend) +
  labs(title = "Seasonally adjusted Naive forecast", y = "Bricks")

```

#### tourism contains quarterly visitor nights (in thousands) from 1998 to 2017 for 76 regions of Australia.

#### Extract data from the Gold Coast region using filter() and aggregate total overnight trips (sum over Purpose) using summarise(). Call this new dataset gc_tourism.

```{r q120} 

gc_tourism <- tourism |>
  filter(Region == "Gold Coast") |>
  group_by(Purpose) |>
  summarise(Total_Overnight_Trips = sum(Trips, na.rm = TRUE))

range(gc_tourism$Quarter)

gc_train_1 <- gc_tourism |>
  slice(1:(n()-4))

gc_train_2 <- gc_tourism |>
  slice(1:(n()-8))

gc_train_3 <- gc_tourism |>
  slice(1:(n()-12))

gc_train_1
gc_train_2
gc_train_3

```
#### Compute one year of forecasts for each training set using the seasonal naïve (SNAIVE()) method. Call these gc_fc_1, gc_fc_2 and gc_fc_3, respectively.

```{r q121} 

gc_tourism <- tourism |>
  filter(Region == "Gold Coast") |>
  group_by(Purpose) |>
  summarise(Total_Overnight_Trips = sum(Trips, na.rm = TRUE))

range(gc_tourism$Quarter)

gc_train_1 <- gc_tourism |>
  slice(1:(n()-4))

gc_train_2 <- gc_tourism |>
  slice(1:(n()-8))

gc_train_3 <- gc_tourism |>
  slice(1:(n()-12))

gc_train_1
gc_train_2
gc_train_3

gc_fc_1 <- gc_train_1 |>
  model(SNAIVE(Total_Overnight_Trips)) |>
  forecast( h = 4) 

gc_fc_1 |>
  autoplot(gc_train_1) +
  labs(title = "GC Train 1 SNaive Forecast")

gc_fc_2 <- gc_train_2 |>
  model(SNAIVE(Total_Overnight_Trips)) |>
  forecast( h = 4)

gc_fc_2 |> autoplot(gc_train_2) +
  labs(title = "GC Train 2 SNaive Forecast")

gc_fc_3 <- gc_train_3 |>
  model(SNAIVE(Total_Overnight_Trips)) |>
  forecast( h = 4) 

gc_fc_3 |>   autoplot(gc_train_3) +
  labs(title = "GC Train 3 SNaive Forecast")

gc_fc_1 |> accuracy(gc_tourism)

gc_fc_2 |> accuracy(gc_tourism)

gc_fc_3 |> accuracy(gc_tourism)

```
<p> It's clear that the gc_fc_3 has the lowest MAPE. This is due removing the last 3 years of observations. </p>