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Bagging exponential smoothing methods using STL decomposition and Box–Cox transformation

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  • Bergmeir, Christoph
  • Hyndman, Rob J.
  • Benítez, José M.

Abstract

Exponential smoothing is one of the most popular forecasting methods. We present a technique for the bootstrap aggregation (bagging) of exponential smoothing methods, which results in significant improvements in the forecasts. The bagging uses a Box–Cox transformation followed by an STL decomposition to separate the time series into the 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. An ensemble of exponential smoothing models is then estimated on the bootstrapped series, and the resulting point forecasts are combined. We evaluate this new method on the M3 data set, and show that it outperforms the original exponential smoothing models consistently. On the monthly data, we achieve better results than any of the original M3 participants.

Suggested Citation

  • Bergmeir, Christoph & Hyndman, Rob J. & Benítez, José M., 2016. "Bagging exponential smoothing methods using STL decomposition and Box–Cox transformation," International Journal of Forecasting, Elsevier, vol. 32(2), pages 303-312.
  • Handle: RePEc:eee:intfor:v:32:y:2016:i:2:p:303-312
    DOI: 10.1016/j.ijforecast.2015.07.002
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    References listed on IDEAS

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    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.
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