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