Forecast Combination Under Heavy-Tailed Errors

Abstract

Forecast combination has been proven to be a very important technique to obtain accurate predictions. In many applications, forecast errors exhibit heavy tail behaviors for various reasons. Unfortunately, to our knowledge, little has been done to deal with forecast combination for such situations. The familiar forecast combination methods such as simple average, least squares regression, or those based on variance-covariance of the forecasts, may perform very poorly. In this paper, we propose two nonparametric forecast combination methods to address the problem. One is specially proposed for the situations that 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 shortage of data and/or evolving data generating process. Adaptive risk bounds of both methods are developed. Simulations and a real example show superior performance of the new methods.