Consider the US quarterly real gross national product from the first quar-
ter of 1947 to the third quarter of 2011. The data are in the file q-GNPC96 txt,
seasonally adjusted, and in billions of chained 2005 dollars. Let xt be the
growth rate series of the real GDP.
The ar command identifies an AR(4) model for xt via the AIC cri-
terion. Fit the model. Is the model adequate? Why?
The sample PACF of xt specifies an AR(3) model. Fit the model. Is
it adequate? Why?
What is the model for xt if one uses in-sample model comparison?
Why?
Divide the data into estimation and forecasting subsamples using
the fourth quarter of 2000 as the initial forecast origin and apply the
backtesting procedure with MSFE as the criterion. Select a model
for xt. Justify the choice.
To answer questions in Problems 3, (a) use 5% significance level in
tests, and (b) use 10 lags of serial correlations for return series.