Question $3$

$3.$Data set global$\_$economy contains the annual Exports from many countries. Select one country to analyse.

a$.$ Plot the Exports series and discuss the main features of the data.

b$.$ Use an ETS$($A$,$N$,$N$)$ model to forecast the series, and plot the forecasts.

c$.$ Compute the RMSE values for the training data.

d$.$ Compare the results to those from an ETS$($A$,$A$,$N$)$ model. $($Remember that the trended model is using one more parameter than the simpler model.$)$ Discuss the merits of the two forecasting methods for this data set.

e$.$ Compare the forecasts from both methods. Which do you think is best?

f$.$ Calculate a $95\%$ prediction interval for the first forecast for each model, using the RMSE values and assuming normal errors. Compare your intervals with those produced using R$.$