Model selection for long-memory processes in the spectral domain

In this paper, we study a novel empirical criterion for identifying the type of a long-memory time series. The proposed rule for selecting an underlying model suitable to the data is based on the comparison between the normalized prediction errors of the generalized Whittle estimator (a parametric spectral estimator) applied to two or more candidate models. We test this approach by two applications of the procedure: for comparing two distinct statistical models to adjust the data, and for assessing the significance of increasing the number of parameters within a given class of models. Due to the heuristic nature of the method, we test the statistic numerically for several classes of stochastic processes, namely Gaussian processes with long-range dependence (LRD), M/G/∞ (non-Gaussian) processes with LRD, non-stationary processes, and non-linear heteroscedastic models. The numerical results demonstrate that the proposed statistic exhibits good power, is robust and not computationally expensive.