Testing for Hermite Rank in Gaussian Subordination Processes

Abstract

Statistical inference for time series with long-range dependence is often based on the assumption of Gaussian subordination Xt = G(Zt). Although the Hermite rank m of G plays an essential role for statistical inference in these situations, the question of estimating m or of testing hypotheses about the Hermite rank has not been addressed in the literature. In this article, a method is introduced for testing H0: m = 1 against H1: m > 1. This allows for deciding whether inference based on the usual assumption of m = 1 is appropriate. Simulations and data examples illustrate the method.