Consider the quarterly real GDP of United Kingdom, Canada, and the United States from the first quarter of 1980 to the second quarter of 2011. The data are available from the Federal Reserve Bank of St. Louis (FRED). Let \(z_{t}\) be the \(\log\) GDP series.

(a) Information criteria suggest a VAR(3) model for \(z_{t}\). Based on a \(\operatorname{VAR}(3)\) model, is the series \(z_{t}\) cointegrated at the \(5 \%\) level? Why?

(b) How many cointegrating vectors are there? Write down the cointegrating vector, if any.

(c) Compute the cointegrated series \(\boldsymbol{w}_{t}\) if any. Perform univariate unit-root test to confirm the stationarity of the components of \(\boldsymbol{w}_{t}\). Draw your conclusion at the \(5 \%\) significance level.

(d) Build an ECM-VAR model for \(\boldsymbol{z}_{t}\). Perform model checking and write down the fitted model.