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Combining Nonparametric and Optimal Linear Time Series Predictions

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  • Sophie DABO-NIANG

    (Crest)

  • Christian FRANCQ

    (Crest)

  • Jean-Michel ZAKOIAN

    (Crest)

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.

Suggested Citation

  • Sophie DABO-NIANG & Christian FRANCQ & Jean-Michel ZAKOIAN, 2009. "Combining Nonparametric and Optimal Linear Time Series Predictions," Working Papers 2009-18, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2009-18
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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. 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.
    3. 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.
    4. 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 for Research in Economics, Yale University.
    5. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1046-1093, December.
    6. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
    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. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    9. 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, March.
    10. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    11. Kreiss, Jens-Peter & Neumann, Michael H. & Yao, Qiwei, 2008. "Bootstrap tests for simple structures in nonparametric time series regression," LSE Research Online Documents on Economics 24135, London School of Economics and Political Science, LSE Library.
    12. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    13. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    14. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    15. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
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    3. Ardelean, Vlad & Pleier, Thomas, 2013. "Outliers & predicting time series: A comparative study," FAU Discussion Papers in Economics 05/2013, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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