Consider the U.S. quarterly gross private saving (GPSAVE) and gross private domestic investment (GPDI) from first quarter of 1947 to the third quarter of 2012. The data are from the Federal Reserve Bank of St. Louis and are in billions of dollars. See the file m-gpsavedi.txt.

- Construct the growth series by taking the first difference of the log data. Denote the growth series by \(z_{t}\). Plot the growth series.

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

- Perform a chi-square test to confirm that one can remove the insignificant parameters in the previous question. You may use 5\% significant level.

- Obtain the impulse response functions of the fitted model. What is the relationship between the private investment and saving?

- Obtain one-step to eight-step ahead predictions of \(z_{t}\) at the forecast origin 2012.III (last data point).

- Obtain the forecast error variance decomposition.