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Understanding exponential smoothing via kernel regression

Author

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

Abstract

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. 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.
    2. 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.
    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. 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.
    5. Ralf Becker & Adam Clements & Robert O'Neill, 2010. "A Kernel Technique for Forecasting the Variance-Covariance Matrix," NCER Working Paper Series 66, National Centre for Econometric Research.
    6. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
    7. Reham Alhindawi & Yousef Abu Nahleh & Arun Kumar & Nirajan Shiwakoti, 2020. "Projection of Greenhouse Gas Emissions for the Road Transport Sector Based on Multivariate Regression and the Double Exponential Smoothing Model," Sustainability, MDPI, vol. 12(21), pages 1-18, November.
    8. 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.
    9. James Brooks & Irena Grugulis & Hugh Cook, 2020. "Rethinking Situated Learning: Participation and Communities of Practice in the UK Fire and Rescue Service," Work, Employment & Society, British Sociological Association, vol. 34(6), pages 1045-1061, December.
    10. Ralf Becker & Adam Clements & Robert O'Neill, 2018. "A Multivariate Kernel Approach to Forecasting the Variance Covariance of Stock Market Returns," Econometrics, MDPI, vol. 6(1), pages 1-27, February.
    11. 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.
    12. 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.
    13. Taylor, James W. & Jeon, Jooyoung, 2015. "Forecasting wind power quantiles using conditional kernel estimation," Renewable Energy, Elsevier, vol. 80(C), pages 370-379.
    14. 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.
    15. Taylor, James W., 2008. "Exponentially weighted information criteria for selecting among forecasting models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 513-524.
    16. 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.
    17. Croux, C. & Fried, R. & Gijbels, I. & Mahieu, K., 2010. "Robust Forecasting of Non-Stationary Time Series," Other publications TiSEM 94542b5e-4319-4f5a-bc35-2, Tilburg University, School of Economics and Management.
    18. 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).
    19. 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.
    20. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    21. 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.
    22. 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.

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