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Combining parametric and nonparametric approaches for more efficient time series prediction

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

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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File URL: http://mpra.ub.uni-muenchen.de/16893/
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Bibliographic 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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Keywords: ARMA representation; noisy data; Nonparametric regression; optimal prediction;

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  1. 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.
  2. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  3. Raymond J Carroll & Oliver Linton & Enno Mammen & Zhijie Xiao, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," STICERD - Econometrics Paper Series /2002/435, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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.
  5. 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.
  6. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers 1585, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. 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.
  9. Christian Francq & Jean-Michel Zakoïan, 1997. "Covariance Matrix Estimation for Estimators of Mixing Wold's Arma," Working Papers 97-19, Centre de Recherche en Economie et Statistique.
  10. 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.
  11. Francq, Christian & Zako an, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 692-728, October.
  12. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
  13. Dinh Tuan, Pham, 1986. "The mixing property of bilinear and generalised random coefficient autoregressive models," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 291-300, December.
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