Likelihood inference for discriminating between long‐memory and change‐point models

Abstract

We develop a likelihood ratio (LR) test procedure for discriminating between a short‐memory time series with a change‐point (CP) and a long‐memory (LM) time series. Under the null hypothesis, the time series consists of two segments of short‐memory time series with different means and possibly different covariance functions. The location of the shift in the mean is unknown. Under the alternative, the time series has no shift in mean but rather is LM. The LR statistic is defined as the normalized log‐ratio of the Whittle likelihood between the CP model and the LM model, which is asymptotically normally distributed under the null. The LR test provides a parametric alternative to the CUSUM test proposed by Berkes et al. (2006). Moreover, the LR test is more general than the CUSUM test in the sense that it is applicable to changes in other marginal or dependence features other than a change‐in‐mean. We show its good performance in simulations and apply it to two data examples.