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Nonparametric multistep-ahead prediction in time series analysis

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  • Rong Chen
  • Lijian Yang
  • Christian Hafner

Abstract

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"("X" "t"+"k"  |"X" "t" , …,  "X" "t" - "d"+1 ) via nonparametric smoothing of "X" "t"+"k" on ("X" "t" , …, "X" "t" - "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. Copyright 2004 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

Volume (Year): 66 (2004)
Issue (Month): 3 ()
Pages: 669-686

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Handle: RePEc:bla:jorssb:v:66:y:2004:i:3:p:669-686

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Cited by:
  1. 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, July.
  2. 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.
  3. 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.
  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. 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.
  6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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