Consider, again, the \(z_{t}\) series of Problem 6. The time plots show the existence of possible aberrant observations, especially at the beginning of the series. Repeat the analyses of Problem 6, but use the subsample for \(t\) from 201 to 791 .

Data from Problem 6

Consider four components of U.S. monthly industrial production index from January 1947 to December 2012 for 792 data points. The four components are durable consumer goods (IPDCONGD), nondurable consumer goods (IPNCONGD), business equivalent (IPBUSEQ), and materials (IPMAT). The original data are from the Federal Reserve Bank of St. Louis and are seasonally adjusted. See the file m-ip4comp.txt.

- Construct the growth rate series \(z_{t}\) of the four industrial production index, that is, take the first difference of the log data. Obtain time plots of \(\boldsymbol{z}_{t}\). Comment on the time plot.

- Build a VAR model for \(z_{t}\), including simplification and model checking. Write down the fitted model.

- Compute one-step to six-step ahead predictions of \(z_{t}\) at the forecast origin \(h=791\) (December 2012). Obtain 95% interval forecasts for each component series.