That is, the mean, variance and covariance are invariant to the time origin. We could use a t-statistic to test the hypothesis This is a legitimate test since the null is a refutable hypothesis, even though the power against a local alternate is negligible. But suppose that the data was really generated by Upon recursive substitution this can be rewritten as which is nonstationary since as t gets large. There is a problem, however, since the center of mass of the usual estimator would be bounded away from 1. We would tend to err on the side of rejecting too many H 0 .
Regression models containing such nonstationary series are meaningless.
Now all errors are permanent. We will leave case 4 until the chapter on cointegration. We have seen this idea of a stochastic intercept elsewhere. Namely in the random effects model. In any event, our test of hypothesis is The test statistic we use for the test of hypothesis is constructed as a t-statistic.