Nonparametric Beta kernel estimator for long memory time series
AbstractThe paper introduces a new nonparametric estimator of the spectral density that is given in smoothing the periodogram by the probability density of Beta random variable (Beta kernel). 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 suggest that the estimator automaticaly adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also 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 reasonable performance of the estimation, and show that the data-driven estimator is a valuable tool for the detection of long-memory as well as hidden periodicities in stock returns.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2011004.
Date of creation: 01 Jan 2011
Date of revision:
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spectral density; long range dependence; nonparametric estimation; periodogram; kernel smoothing; Beta kernel; cross-validation;
Other versions of this item:
- Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," IDEI Working Papers 633, Institut d'Économie Industrielle (IDEI), Toulouse.
- Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," TSE Working Papers 09-082, Toulouse School of Economics (TSE).
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-05-14 (All new papers)
- NEP-ECM-2011-05-14 (Econometrics)
- NEP-ETS-2011-05-14 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
- Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, December.
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