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The max log likellihood function is simply a function of the error covariance matrix

The max log likellihood function is simply a function of the error covariance matrix + constant terms!. The max of the log likelihood function:. Proof:. The distribution of the ML estimates:. The covariance matrix. The unrestricted VAR(2). ECM representations. Ecm with m=1.

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The max log likellihood function is simply a function of the error covariance matrix

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

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

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

  4. The unrestricted VAR(2)

  5. ECM representations

  6. Ecm with m=1

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

  8. Ecm with m=2

  9. Ecm in acceleration rates, changes and levels

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

  11. The relationship between the ECM parameters

  12. Misspecification tests

  13. Information criteria

  14. Choice of lag length

  15. Trace correlation = 0.40

  16. Tests of residual autocorrelation

  17. Tests of residual heteroscedasticity

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

  19. Univariate Normality tests

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

  21. Approximate normality tests

  22. Multivariate Bowman-Shenton normality test

  23. What about the other tests?

  24. The univariate normality tests

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