Testing for a change of the long-memory parameter

Long-range dependence is often observed in long time series. Correlations decay approximately like |k|2H-2, with H ε (0.5, 1), as the lag k tends to infinity. The long-term features of the data are essentially characterised by the parameter H. Small changes of H have strong implications for the long-term behaviour of the process. In particular, rates of convergence of estimators for the mean, and for many other parameters of interest, differ for different values of H. For some data sets, H appears to change with time. In this paper we consider a simple test of the null hypothesis that H is constant. The test is based on a functional central limit theorem for quadratic forms. Critical values for the test statistic are given. Simulations confirm the validity of the test. A data example illustrates its practical application.