Coefficient constancy test in AR-ARCH models

In this article, we consider the problem of testing the coefficient constancy in the AR-ARCH model: yt=([phi]+bt)yt-1+[var epsilon]t, where [var epsilon]t=[eta]t-1[xi]t, [eta]t-1=([alpha]0+[alpha]1[var epsilon]t-12)1/2 and [xi]t are iid r.v.'s. Under the assumption that bt and [xi]t are Gaussian, a locally best invariant test is provided for testing whether bt are identically zero or not. Since the exact distribution of the test statistic is hard to obtain, its limiting distribution is investigated. It is shown that the test statistic depends upon the parameter estimators and is asymptotically normal under the null hypothesis.