Consider the US quarterly real gross national product from the first quarter of 1947 to the third
Question:
Consider the US quarterly real gross national product from the first quarter 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 \(x_{t}\) be the growth rate series of the real GDP.
(a) The ar command identifies an AR(4) model for \(x_{t}\) via the AIC criterion. Fit the model. Is the model adequate? Why?
(b) The sample PACF of \(x_{t}\) specifies an \(\mathrm{AR}(3)\) model. Fit the model. Is it adequate? Why?
(c) What is the model for \(x_{t}\) if one uses in-sample model comparison? Why?
(d) 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 \(x_{t}\). Justify the choice.
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