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Combining parametric and nonparametric approaches for more efficient time series prediction

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Author Info
Dabo-Niang, Sophie
Francq, Christian
Zakoian, Jean-Michel

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Abstract

We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process. We establish consistency and asymptotic normality results for our estimator. A Monte Carlo study and an empirical application on stock market indices suggest that significant gains can be achieved with our approach.

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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16893.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:16893

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Related research
Keywords: ARMA representation; noisy data; Nonparametric regression; optimal prediction;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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.:
  1. Anton Schick & Wolfgang Wefelmeyer, 2004. "Root "n" consistent and optimal density estimators for moving average processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 31(1), pages 63-78. [Downloadable!] (restricted)
  2. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November. [Downloadable!] (restricted)
  3. Zhijie Xiao & Oliver Linton & Raymond J. Carroll & E. Mammen, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," Cowles Foundation Discussion Papers 1375, Cowles Foundation, Yale University. [Downloadable!]
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  4. Hall, Peter & Yatchew, Adonis, 2005. "Unified approach to testing functional hypotheses in semiparametric contexts," Journal of Econometrics, Elsevier, vol. 127(2), pages 225-252, August. [Downloadable!] (restricted)
  5. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin. [Downloadable!]
  6. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February. [Downloadable!]
  7. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November. [Downloadable!] (restricted)
  8. Christian Francq ; Jean-Michel Zakoïan, . "Covariance Matrix Estimation for Estimators of Mixing Wold's Arma," Working Papers 97-19, Centre de Recherche en Economie et Statistique. [Downloadable!]
  9. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January. [Downloadable!] (restricted)
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