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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. - PowerPoint PPT Presentation
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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
Interpreting the first row as a disequilibrium error:
from the long-run steady-state relation:
Ecm with m=2
Ecm in acceleration rates, changes and levels
Invariant and variant testsF-tests of ind. Regressors:
m=1
Acceler. Rates:
Log likelihood value identical in all cases!
m=2
VAR
The relationship between the ECM parameters
Misspecification tests
Information criteria
Choice of lag length
Trace correlation
= 0.40
Tests of residual autocorrelation
Tests of residual heteroscedasticity
Normality
• Skewness and excess kurtosis
• Univariate normality tests (Jarque-Bera)
• Mulivariate normallity test (Doornik-Hansen)
Univariate Normality tests
Asymptotic normality tests
Univariate Jarque-Bera type of test:
Multivariate Jarque-Bera type of test:
Approximate normality tests
Multivariate Bowman-Shenton normality test
What about the other tests?
The univariate normality tests
