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

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

2010-12-03

arxiv.org/abs/1012.0690v1

Mathematics

Statistics Theory

Scientific paper

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.

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