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Nonparametric beta kernel estimator for long and short memory time series |
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| Authors: | Taoufik Bouezmarni Sébastien Bellegem Yassir Rabhi |
| Institution: | 1. Département de mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada;2. Economics School of Louvain and Center for operations research and econometrics, Université catholique de Louvain, Louvain-la-Neuve, Belgium;3. Department of Mathematical Sciences, University of Essex, Colchester, U.K |
| Abstract: | 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 |
| Keywords: | Beta kernel smoothing cross-validation long range dependence nonparametric estimation periodogram short memor spectral density |