The cusum of squares test for scale changes in infinite order moving average processes

In this paper we consider the problem of testing for a scale change in the infinite order moving average process X-j = Sigma (infinity)(i=0) a(i)epsilon (j-i,), where epsilon (j) are i.i.d. r.v.s with E \ epsilon (1)\ (alpha) < infinity for some a > 0. In performing the test, a cusum of squares test statistic analogous to Inclan & Tiao's (1994) statistic is considered. It is well-known from the literature that outliers affect test procedures leading to false conclusions. In order to remedy this, a cusum of squares test based on trimmed observations is considered. It is demonstrated that this test is robust against outliers and is valid for infinite variance processes as well. Simulation results are given for illustration.