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

2010/12/03 by Jean‐Marc Bardet, Bardet, Jean-Marc, Hatem Bibi +1
Computer Science · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Fault Detection and Control Systems #Financial Risk and Volatility Modeling #Image and Signal Denoising Methods #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1012.0690

openalex publication_date 2010/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is first devoted to study an adaptive wavelet based estimator of\nthe long memory parameter for linear processes in a general semi-parametric\nframe. This is an extension of Bardet it et al. (2008) which only concerned\nGaussian processes. Moreover, the definition of the long memory parameter\nestimator is modified and asymptotic results are improved even in the Gaussian\ncase. Finally an adaptive goodness-of-fit test is also built and easy to be\nemployed: it is a chi-square type test. Simulations confirm the interesting\nproperties of consistency and robustness of the adaptive estimator and test.\n

Citations

• Convergence of a stochastic approximation version of the EM algorithm

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