(a) Briefly outline Johansen’s methodology for testing for cointegration between a set of variables in the context of a VAR.

(b) A researcher uses the Johansen procedure and obtains the following test statistics (and critical values)

r λmax 5%

critical value 0 38.962 33.178 1 29.148 27.169 2 16.304 20.278 3 8.861 14.036 4 1.994 3.962 Determine the number of cointegrating vectors.

(c) ‘If two series are cointegrated, it is not possible to make inferences regarding the cointegrating relationship using the Engle–Granger technique since the residuals from the cointegrating regression are likely to be autocorrelated.’

How does Johansen circumvent this problem to test hypotheses about the cointegrating relationship?

(d) Give one or more examples from the academic finance literature of where the Johansen systems technique has been employed. What were the main results and conclusions of this research?

(e) Compare the Johansen maximal eigenvalue test with the test based on the trace statistic. State clearly the null and alternative hypotheses in each case.