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Forecast Combination under Heavy-Tailed Errors

Gang Cheng (), Sicong Wang () and Yuhong Yang ()
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Gang Cheng: School of Statistics, University of Minnesota at Twin Cities, 313 Ford Hall, 224 Church Street SE, Minneapolis, MN 55455, USA
Sicong Wang: School of Statistics, University of Minnesota at Twin Cities, 313 Ford Hall, 224 Church Street SE, Minneapolis, MN 55455, USA
Yuhong Yang: School of Statistics, University of Minnesota at Twin Cities, 313 Ford Hall, 224 Church Street SE, Minneapolis, MN 55455, USA

Econometrics, 2015, vol. 3, issue 4, 1-28

Abstract: Forecast combination has been proven to be a very important technique to obtain accurate predictions for various applications in economics, finance, marketing and many other areas. In many applications, forecast errors exhibit heavy-tailed behaviors for various reasons. Unfortunately, to our knowledge, little has been done to obtain reliable forecast combinations for such situations. The familiar forecast combination methods, such as simple average, least squares regression or those based on the variance-covariance of the forecasts, may perform very poorly due to the fact that outliers tend to occur, and they make these methods have unstable weights, leading to un-robust forecasts. To address this problem, in this paper, we propose two nonparametric forecast combination methods. One is specially proposed for the situations in which the forecast errors are strongly believed to have heavy tails that can be modeled by a scaled Student’s t-distribution; the other is designed for relatively more general situations when there is a lack of strong or consistent evidence on the tail behaviors of the forecast errors due to a shortage of data and/or an evolving data-generating process. Adaptive risk bounds of both methods are developed. They show that the resulting combined forecasts yield near optimal mean forecast errors relative to the candidate forecasts. Simulations and a real example demonstrate their superior performance in that they indeed tend to have significantly smaller prediction errors than the previous combination methods in the presence of forecast outliers.

Keywords: forecast combination; heavy tails; robustness; time series models; nonparametric forecast combination (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2015
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