Dummy variables in simple dynamic model

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Which conditions should the expected mean satisfy?
Generally we would like the equilibrium mean to
be equal to zero!
We use the identity
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The case with a constant and a trend
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When there is a linear time trend in the
equations, then
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A simulated example
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Five cases
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The MA representation with determ. comp.
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The MA representation with a trend in the
equations
Linear trends in the variables can derive from
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Dummy variables in the simple dynamic model
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Repetition
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Dummy variables in the CVAR
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Decomposing the dummy variables
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The CVAR model with decomposed dummies can be
written in simplified form
The expected value of the process and the
cointegration relations becomes
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The dynamic properties of the data vector can now
be expressed as
where
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Using the decompositions
It is easy to see that
where
Implying that
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Illustration
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Are the observed outliers additive or
innovational?
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An additive outlier in real money stock
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The Danish VAR model with trend and dummy
variables
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We need to distinguish between
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How sensitive are the CVAR results to outliers?