Change point detection with stable AR(1) errors

In this paper we develop two types of tests to detect changes in the location parameters of dependent observations with infinite variances. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. If the d largest (in magnitude) observations are removed from the sample, then the standard CUSUM process developed for weakly dependent observations with finite variance can be used assuming that d = d(n)→∞ as n, the sample size tends to ∞. We study two types of statistics. The maximally selected CUSUM process we estimate the long run variance by kernel estimators. We also propose ratio statistics which do not depend on the long run variances. Monte Carlo simulations illustrate the the limit results can be used even in case of small and moderate sample sizes. 1.