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

(a) business equipments and

(b) materials. The data are in columns 5 and 6 of the file m-ip3comp.txt.

(a) Construct the percentage growth rate series of the two components and denote the series by \(\boldsymbol{z}_{t}\).

(b) Build a VARMA model for \(\boldsymbol{z}_{t}\), including model refinements with threshold 1.645 and model checking.

(c) Write down the fitted model. Is there any Granger causality in the fitted model? Why?

(d) Use the fitted model to obtain the one-step to four-step ahead predictions of the two growth rate series.