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Nonparametric beta kernel estimator for long and short memory time series

Bouezmarni, T and Bellegem, S and Rabhi, Y (2020) 'Nonparametric beta kernel estimator for long and short memory time series.' Canadian Journal of Statistics, 48 (3). 582 - 595. ISSN 0319-5724

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In this article we introduce 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. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 19 Aug 2020 15:38
Last Modified: 21 Apr 2021 01:00

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