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Understanding exponential smoothing via kernel regression


  • I. Gijbels
  • A. Pope
  • M. P. Wand


Exponential smoothing is the most common model‐free means of forecasting a future realization of a time series. It requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one‐step‐ahead forecasts. In this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation. We also use theoretical developments from the kernel regression field to derive, for the first time, asymptotic properties of exponential smoothing forecasters.

Suggested Citation

  • I. Gijbels & A. Pope & M. P. Wand, 1999. "Understanding exponential smoothing via kernel regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 39-50.
  • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:39-50
    DOI: 10.1111/1467-9868.00161

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    Cited by:

    1. Fan, Jianqing & Fan, Yingying & Jiang, Jiancheng, 2007. "Dynamic Integration of Time- and State-Domain Methods for Volatility Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 618-631, June.
    2. Catalin Starica, 2004. "Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?," Econometrics 0411015, University Library of Munich, Germany.
    3. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
    4. Hart, Jeffrey D. & Lee, Cherng-Luen, 2005. "Robustness of one-sided cross-validation to autocorrelation," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 77-96, January.
    5. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    6. Croux, C. & Fried, R. & Gijbels, I. & Mahieu, K., 2010. "Robust Forecasting of Non-Stationary Time Series," Discussion Paper 2010-105, Tilburg University, Center for Economic Research.
    7. K De Brabanter & F Cao & I Gijbels & J Opsomer, 2018. "Local polynomial regression with correlated errors in random design and unknown correlation structure," Biometrika, Biometrika Trust, vol. 105(3), pages 681-690.
    8. Ralf Becker & Adam Clements & Robert O'Neill, 2018. "A Multivariate Kernel Approach to Forecasting the Variance Covariance of Stock Market Returns," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-27, February.
    9. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    10. Taylor, James W., 2008. "Exponentially weighted information criteria for selecting among forecasting models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 513-524.
    11. Taylor, James W. & Jeon, Jooyoung, 2015. "Forecasting wind power quantiles using conditional kernel estimation," Renewable Energy, Elsevier, vol. 80(C), pages 370-379.
    12. Jungwoo Kim & Joocheol Kim, 2017. "Nonparametric forecasting with one-sided kernel adopting pseudo one-step ahead data," Working papers 2017rwp-102, Yonsei University, Yonsei Economics Research Institute.
    13. J Keith Ord & Ralph D Snyder & Anne B Koehler & Rob J Hyndman & Mark Leeds, 2005. "Time Series Forecasting: The Case for the Single Source of Error State Space," Monash Econometrics and Business Statistics Working Papers 7/05, Monash University, Department of Econometrics and Business Statistics.
    14. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
      • 1, 2015. "," Working Papers 15/02, Department of Economics, City University London.
    15. Marcel Dettling & Peter Buhlmann, 2004. "Volatility and risk estimation with linear and nonlinear methods based on high frequency data," Applied Financial Economics, Taylor & Francis Journals, vol. 14(10), pages 717-729.
    16. Daniel C Medina & Sally E Findley & Boubacar Guindo & Seydou Doumbia, 2007. "Forecasting Non-Stationary Diarrhea, Acute Respiratory Infection, and Malaria Time-Series in Niono, Mali," PLOS ONE, Public Library of Science, vol. 2(11), pages 1-13, November.
    17. Choi, Jaesung & Roberts, David C. & Lee, Eunsu, 2014. "Forecast of CO2 Emissions From the U.S. Transportation Sector: Estimation From a Double Exponential Smoothing Model," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 53(3), pages 1-20.
    18. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.

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