Consider the U.S. monthly personal consumption expenditures (PCE) and disposable personal income (DSPI) from January 1959 to March 2012. The data are from FRED of the Federal Reserve Bank of St. Louis, in billions of dollars, and seasonally adjusted. Let \(z_{t}\) be the log series of PCE and DSPI. Data are also in the files m-pee.txt and m-dspi.txt.

(a) Are the components of \(z_{t}\) cointegrated? Why?

(b) What is the cointegrating vector, if any?

(c) Perform univariate analysis of the cointegrated series to confirm its stationarity.

(d) Build an ECM-VAR model for \(\boldsymbol{z}_{t}\), including model checking. Write down the fitted model.