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

TL;DR

This paper introduces an adaptive wavelet-based estimator for the long memory parameter in linear processes, extending previous Gaussian-focused methods, and develops a chi-square goodness-of-fit test with confirmed consistency and robustness.

Contribution

It extends wavelet-based long memory estimation to general linear processes and improves asymptotic results, also providing an easy-to-use adaptive goodness-of-fit test.

Findings

Estimator shows consistency and robustness in simulations

Improved asymptotic properties even for Gaussian processes

Developed a practical chi-square goodness-of-fit test

Abstract

This paper is first devoted to study an adaptive wavelet based estimator of the long memory parameter for linear processes in a general semi-parametric frame. This is an extension of Bardet {\it et al.} (2008) which only concerned Gaussian processes. Moreover, the definition of the long memory parameter estimator is modified and 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.