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Combining Nonparametric and Optimal Linear Time Series Predictions

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  • Dabo-Niang, Sophie
  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

We introduce a semiparametric procedure for more efficient prediction of a strictly stationaryprocess admitting an ARMA representation. The procedure is based on the estimation of the ARMArepresentation, followed by a nonparametric regression where the ARMA residuals are used as explanatoryvariables. Compared to standard nonparametric regression methods, the number of explanatory variablescan be reduced because our approach exploits the linear dependence of the process. We establish consistencyand asymptotic normality results. A Monte Carlo study and an empirical application on stockindices suggest that significant gains can be achieved with our approach.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 105 (2010)
Issue (Month): 492 ()
Pages: 1554-1565

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Handle: RePEc:bes:jnlasa:v:105:i:492:y:2010:p:1554-1565

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References

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  1. 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.
  2. 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 & Swedish Statistical Association, vol. 31(1), pages 63-78.
  3. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  4. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  5. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers 1585R, Cowles Foundation for Research in Economics, Yale University, revised Nov 2006.
  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.
  7. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
  8. 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.
  9. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
  10. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74145, Tilburg University.
  11. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  12. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1046-1093, December.
  13. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
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Cited by:
  1. Ardelean, Vlad & Pleier, Thomas, 2013. "Outliers & predicting time series: A comparative study," IWQW Discussion Paper Series 05/2013, Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW).

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