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Forecasting: Principles and Practice

Preface

$1$ Getting started

$2$ Time series graphics

$3$ Time series decomposition

$4$ Time series features

$5$ The forecasters toolbox

$5\mathrm{.}1$ A tidy forecasting workflow

$5\mathrm{.}2$ Some simple forecasting methods

$5\mathrm{.}3$ Fitted values and residuals

$5\mathrm{.}4$ Residual diagnostics

$5\mathrm{.}5$ Distributional forecasts and prediction intervals

$5\mathrm{.}6$ Forecasting using transformations

$5\mathrm{.}7$ Forecasting with decomposition

$5\mathrm{.}8$ Evaluating point forecast accuracy

$5\mathrm{.}9$ Evaluating distributional forecast accuracy

$5\mathrm{.}10$ Time series cross$-$validation

$5\mathrm{.}11$ Exercises

$5\mathrm{.}12$ Further reading

$6$ Judgmental forecasts

$7$ Time series regression models

$8$ Exponential smoothing

$9$ ARIMA models

$10$ Dynamic regression models

$11$ Forecasting hierarchical and grouped time series

$12$ Advanced forecasting methods

$13$ Some practical forecasting issues

Appendix: Using R

Appendix: For instructors

Appendix: Reviews

Translations

About the authors

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Bibliography

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$5\mathrm{.}11$ Exercises

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$).$

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?

Apply a seasonal nave 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.

# 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$)$

What do you conclude?

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.

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?

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

Good forecast methods should have normally distributed residuals.

A model with small residuals will give good forecasts.

The best measure of forecast accuracy is MAPE.

If your model doesnt forecast well, you should make it more complicated.

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

For your retail time series $($from Exercise $7$ in Section $2\mathrm{.}10)$:

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

myseries$\_$train $<-$ myseries $|>$

filter$($year$($Month$)<2011)$

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

autoplot$($myseries$,$ Turnover$)+$

autolayer$($myseries$\_$train, Turnover, colour $=$ "red"$)$

Fit a seasonal nave model using SNAIVE$()$ applied to your training data $($myseries$\_$train$).$

fit $<-$ myseries$\_$train $|>$

model$($SNAIVE$())$

Check the residuals.

fit $|>$ gg$\_$tsresiduals$()$

Do the residuals appear to be uncorrelated and normally distributed?

Produce forecasts for the test data

fc $<-$ fit $|>$

forecast$($new$\_$data $=$ anti$\_$join$($myseries$,$ myseries$\_$train$))$

fc $|>$ autoplot$($myseries$)$

Compare the accuracy of your forecasts against the actual values.

fit $|>$ accuracy$()$

fc $|>$ accuracy$($myseries$)$

How sensitive are the accuracy measures to the amount of training data used?

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$.$

Create a training set of $486$ observations, withholding a test set of $72$ observations $(6$ years$).$

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

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

Create a training set for household wealth $($hh$\_$budget$)$ by withholding the last four years as a test set.

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

Compute the accuracy of your forecasts. Which method does best?

Do the residuals from the best method resemble white noise?

Create a training set for Australian takeaway food turnover $($aus$\_$retail$)$ by withholding the last four years as a test set.

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

Compute the accuracy of your forecasts. Which method does best?

Do the residuals from the best method resemble white noise?

We will use the Bricks data from aus$\_$production $($Australian quarterly clay brick production $19562005)$ for this exercise.

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

Compute and plot the seasonally adjusted data.

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

Use decomposition$\_$model$()$ to reseasonalise the results, giving forecasts for the original data.

Do the residuals look uncorrelated?

Repeat with a robust STL decomposition. Does it make much difference?

Compare forecasts from decomposition$\_$model$()$ with those from SNAIVE$(),$ using a test set comprising the last $2$ years of data. Which is better?