3. The max log likellihood function is simply a function of the error covariance matrix + constant terms!

4. The max of the log likelihood function: Proof:

6. The distribution of the ML estimates: The covariance matrix

9. The unrestricted VAR(2)

11. ECM representations

12. Ecm with m=1

13. Interpreting the first row as a disequilibrium error: from the long-run steady-state relation:

14. Ecm with m=2

15. Ecm in acceleration rates, changes and levels

16. Invariant and variant tests F-tests of ind. Regressors: m=1 Acceler. Rates: Log likelihood value identical in all cases! m=2 VAR

17. The relationship between the ECM parameters

19. Misspecification tests

25. Information criteria

26. Choice of lag length

28. Trace correlation = 0.40

29. Tests of residual autocorrelation

30. Tests of residual heteroscedasticity

31. Normality Skewness and excess kurtosis Univariate normality tests (Jarque-Bera) Mulivariate normallity test (Doornik- Hansen)

32. Univariate Normality tests

33. Asymptotic normality tests Univariate Jarque-Bera type of test: Multivariate Jarque-Bera type of test:

34. Approximate normality tests

36. Multivariate Bowman-Shenton normality test

37. What about the other tests?

38. The univariate normality tests