Consider two components of U.S. monthly industrial production index from December 1963 to December 2012. The two components are

(a) nondurable consumer goods and

(b) materials. The data are in columns 3 and 6 of the file m-ip3comp.txt and are obtained from the Federal Reserve Bank of St. Louis.

(a) Construct the percentage growth rate series of the two components, that is, first difference of the log data times 100 . Denote the series by \(\boldsymbol{z}_{t}\).

(b) Specify a simple VARMA model for \(\boldsymbol{z}_{t}\) using \(5 \%\) as the type I error.

(c) Fit the specified model and remove the parameter estimates with \(t\)-ratios less than 1.96. Write down the fitted model.

(d) Perform model checking of the fitted model. Is the model adequate? Why?

(e) Compute the impulse response functions of the fitted model.