Testing parameter constancy in linear models against stochastic stationary parameters

This paper considers testing parameter constancy in a linear model when the alternative is that a subset of the parameters follows a stationary vector autoregressive process of known finite order. This kind of a linear model is only identified under the alternative, which usually precludes finding a test statistic with an analytic null distribution. In the present situation, however, it is still possible to derive a test statistic with an asymptotic chi-squared distribution under the null hypothesis and this is done in the paper. The small-sample properties of the test statistic are investigated by simulation and found statisfactory. The test retains its power when the alternative to parameter constancy is a random walk parameter process.