DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

Abstract

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I (d) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I (d1) to I (d2), −.5 < d1 < d2. We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests (see Kwiatkowski, Phillips, Schmidt and Shin, 1992) considered in some previous works.