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Nonparametric multistep‐ahead prediction in time series analysis

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  • Rong Chen
  • Lijian Yang
  • Christian Hafner

Abstract

Summary. We consider the problem of multistep‐ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non‐linear time series models have certain advantages in multistep‐ahead forecasting. Traditionally, nonparametric k‐step‐ahead least squares prediction for non‐linear autoregressive AR(d) models is done by estimating E(Xt+k |Xt, …, Xt−d+1) via nonparametric smoothing of Xt+k on (Xt, …, Xt−d+1) directly. We propose a multistage nonparametric predictor. We show that the new predictor has smaller asymptotic mean‐squared error than the direct smoother, though the convergence rate is the same. Hence, the predictor proposed is more efficient. Some simulation results, advice for practical bandwidth selection and a real data example are provided.

Suggested Citation

  • Rong Chen & Lijian Yang & Christian Hafner, 2004. "Nonparametric multistep‐ahead prediction in time series analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 669-686, August.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:3:p:669-686
    DOI: 10.1111/j.1467-9868.2004.04664.x
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    Cited by:

    1. Souhaib Ben Taieb & Rob J Hyndman, 2012. "Recursive and direct multi-step forecasting: the best of both worlds," Monash Econometrics and Business Statistics Working Papers 19/12, Monash University, Department of Econometrics and Business Statistics.
    2. Tschernig, Rolf & Yang, Lijian, 2000. "Nonparametric estimation of generalized impulse response function," SFB 373 Discussion Papers 2000,89, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2013. "Nonparametric Estimation and Parametric Calibration of Time-Varying Coefficient Realized Volatility Models," Monash Econometrics and Business Statistics Working Papers 21/13, Monash University, Department of Econometrics and Business Statistics.
    5. Cao, Yanrong & Lin, Haiqun & Wu, Tracy Z. & Yu, Yan, 2010. "Penalized spline estimation for functional coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 891-905, April.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    7. Heejoon Han & Shen Zhang, 2012. "Non‐stationary non‐parametric volatility model," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 204-225, June.
    8. Bontempi, Gianluca & Ben Taieb, Souhaib, 2011. "Conditionally dependent strategies for multiple-step-ahead prediction in local learning," International Journal of Forecasting, Elsevier, vol. 27(3), pages 689-699.
    9. Tracy Wu & Haiqun Lin & Yan Yu, 2011. "Single-index coefficient models for nonlinear time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 37-58.
    10. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2018. "Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 88-100, January.
    11. Dimitris N. Politis & Kejin Wu, 2023. "Multi-Step-Ahead Prediction Intervals for Nonparametric Autoregressions via Bootstrap: Consistency, Debiasing, and Pertinence," Stats, MDPI, vol. 6(3), pages 1-29, August.
    12. Loïc Maréchal, 2021. "Do economic variables forecast commodity futures volatility?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1735-1774, November.

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