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