Consider, again, the annual real gross domestic products per capita for United States. and United Kingdom of Problem 6. Use multivariate exponential smoothing to produce one-step ahead forecasts of the two real GDP series at the forecast origin year 2011 .

Data from Problem 6

Consider the annual real gross domestic products per capita of four OECD countries. The countries are (a) United States, (b) Germany, (c) United Kingdom, and (d) France. The real GDP are in 2011 U.S. dollars, and the sample period is from 1960 to 2011 for 52 observations. The data are available from FRED of the Federal Reserve Bank of St. Louis and in the file a-rgdp-per-4. txt. Let \(\boldsymbol{z}_{t}\) be the \(\log\) series of the data.

Use \(K=2\) to perform cointegration tests. Are the log gdp series cointegrated? Why?

What is the cointegrating vector, if any?

Perform unit-root test to confirm the stationarity of the cointegrated process.

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