Applicability of the Whittle estimator to non-stationary and non-linear long-memory processes

The Whittle estimator is a classic statistic to measure the long‐memory parameter of stationary stochastic processes. Recently, the theoretical framework of the estimator has been extended to include its application to non‐linear and non‐stationary processes. The asymptotic behaviour of the generalized estimator has been analysed in several works, but there seems to be limited empirical studies about the robustness of the estimator on real or synthetic time series. In this paper, we test the robustness of the general Whittle estimator applied to some classes of non‐stationary and non‐linear long‐memory processes. We evaluate the bias and variance of the estimator of the long‐memory parameter for different combinations of the correlation parameters and the sample sizes. The numerical results obtained indicate that the performance of the estimator is good, but the sample length necessary to obtain good estimations depends on the type of process and the degree of short and long‐term correlation.