Adaptive semiparametric wavelet estimator and goodness-of-fit test for long-memory linear processes

Abstract

This paper is first devoted to the study of an adaptive wavelet-based estimator of the long-memory parameter for linear processes in a general semiparametric frame. As such this is an extension of the previous contribution of Bardet et al. (2008) which only concerned Gaussian processes. Moreover, the definition of the long-memory parameter estimator has been modified and the asymptotic results are improved even in the Gaussian case. Finally an adaptive goodness-of-fit test is also built and easy to be employed: it is a chi-square type test. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimator and test.