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
