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Nonparametric Beta Kernel Estimator for Long and Short Memory Time Series

Bouezmarni, Taoufik and Van Bellegem, Sebastien and Rabhi, Yassir (2020) 'Nonparametric Beta Kernel Estimator for Long and Short Memory Time Series.' The Canadian Journal of Statistics, 48 (3). pp. 582-595. ISSN 0319-5724

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Abstract

In this article we introduces a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long‐ and the short‐range dependency of the process. A cross‐validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator.

Item Type: Article
Uncontrolled Keywords: Statistics & Probability; Beta kernel smoothing; cross-validation; long range dependence; nonparametric estimation; periodogram; short memor; spectral density
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 19 Aug 2020 15:38
Last Modified: 06 Jan 2022 14:13
URI: http://repository.essex.ac.uk/id/eprint/27339

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