The Moving-Estimates Test for Parameter Stability

In this paper a new class of tests for parameter stability, the moving-estimates (ME) test, is proposed. It is shown that in the standard situation the ME test asymptotically equivalent to the maximal likelihood ratio test under the alternative of a temporary parameter shift. It is also shown that the asymptotic null distribution of the ME test is determined by the increments of a vector Brownian bridge and that under a broad class of alternatives the ME test is consistent and has nontrivial local power in general. Our simulations also demonstrate that the proposed test has power superior to other competing tests when parameters are temporarily instable.