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Bagging Exponential Smoothing Methods using STL Decomposition and Box-Cox Transformation

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  • Christoph Bergmeir
  • Rob J Hyndman
  • Jose M Benitez

Abstract

Exponential smoothing is one of the most popular forecasting methods. We present a method for bootstrap aggregation (bagging) of exponential smoothing methods. The bagging uses a Box-Cox transformation followed by an STL decomposition to separate the time series into trend, seasonal part, and remainder. The remainder is then bootstrapped using a moving block bootstrap, and a new series is assembled using this bootstrapped remainder. On the bootstrapped series, an ensemble of exponential smoothing models is estimated. The resulting point forecasts are averaged using the mean. We evaluate this new method on the M3 data set, showing that it consistently outperforms the original exponential smoothing models. On the monthly data, we achieve better results than any of the original M3 participants. We also perform statistical testing to explore significance of the results. Using the MASE, our method is significantly better than all the M3 participants on the monthly data.

Suggested Citation

  • Christoph Bergmeir & Rob J Hyndman & Jose M Benitez, 2014. "Bagging Exponential Smoothing Methods using STL Decomposition and Box-Cox Transformation," Monash Econometrics and Business Statistics Working Papers 11/14, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2014-11
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    References listed on IDEAS

    as
    1. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    2. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    3. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    4. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    5. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    6. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    7. Koning, Alex J. & Franses, Philip Hans & Hibon, Michele & Stekler, H.O., 2005. "The M3 competition: Statistical tests of the results," International Journal of Forecasting, Elsevier, vol. 21(3), pages 397-409.
    8. Paul Goodwin, 2010. "The Holt-Winters Approach to Exponential Smoothing: 50 Years Old and Going Strong," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, issue 19, pages 30-33, Fall.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    bagging; bootstrapping; exponential smoothing; STL decomposition.;
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