## 3.7 Exercises

For the following series, find an appropriate Box-Cox transformation in order to stabilize the variance.

`usnetelec`

`usgdp`

`mcopper`

`enplanements`

Why is a Box-Cox transformation unhelpful for the

`cangas`

data?What Box-Cox transformation would you select for your retail data (from Exercise 1 in Section

**??**)?Calculate the residuals from a seasonal naïve forecast applied to the quarterly Australian beer production data from 1992. The following code will help.

`beer <- window(ausbeer, start=1992) fc <- snaive(beer) autoplot(fc) res <- residuals(fc) autoplot(res)`

Test if the residuals are white noise and normally distributed.

`checkresiduals(fc)`

What do you conclude?

Repeat the exercise for the

`WWWusage`

and`bricksq`

data. Use whichever of`naive`

or`snaive`

is more appropriate in each case.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 doesn’t 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 1 in Section

**??**)?Split the data into two parts using

`x1 <- window(mytimeseries, end=c(2010,12)) x2 <- window(mytimeseries, start=2011)`

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

`autoplot(cbind(x1,x2))`

Calculate forecasts using

`snaive`

applied to`x1`

.Compare the accuracy of your forecasts against the actual values stored in

`x2`

.`f1 <- snaive(x1) accuracy(f1,x2)`

Check the residuals.

`checkresiduals(f1)`

Do the residuals appear to be uncorrelated and normally distributed?

How sensitive are the accuracy measures to the training/test split?

Use the Dow Jones index (data set

`dowjones`

) 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?

Consider the daily closing IBM stock prices (data set

`ibmclose`

).- Produce some plots of the data in order to become familiar with it.
- Split the data into a training set of 300 observations and a test set of 69 observations.
- 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?

Consider the sales of new one-family houses in the USA, Jan 1973 – Nov 1995 (data set

`hsales`

).- Produce some plots of the data in order to become familiar with it.
- Split the
`hsales`

data set into a training set and a test set, where the test set is the last two years of data. - 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?