Detection of non-constant long memory parameter

This article deals with detection of nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with 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 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 considered in some previous works.