We use the identity

Generally we would like the mean of an equilibrium errorto be equal to zero!

Which conditions should the expected cointegration mean satisfy?

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: