Electronic Journal of Statistics

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

Jean-Marc Bardet and Hatem Bibi

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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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 2383-2419.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1356098616

Digital Object Identifier
doi:10.1214/12-EJS754

Mathematical Reviews number (MathSciNet)
MR3020269

Zentralblatt MATH identifier
1295.62082

Subjects
Primary: 62M07: Non-Markovian processes: hypothesis testing 62M09: Non-Markovian processes: estimation
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M15: Spectral analysis 60F05: Central limit and other weak theorems

Keywords
Long range dependence linear processes wavelet estimator semiparametric estimator adaptive estimator adaptive goodness-of-fit test

Citation

Bardet, Jean-Marc; Bibi, Hatem. Adaptive semiparametric wavelet estimator and goodness-of-fit test for long-memory linear processes. Electron. J. Statist. 6 (2012), 2383--2419. doi:10.1214/12-EJS754. https://projecteuclid.org/euclid.ejs/1356098616


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References

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