Regression Approach to the Linear Plus Quadratic Combination of Forecasts

Abstract

In Troschke and Trenkler (2000) the authors introduce linear plus quadratic approaches to the mean square error optimal combination of forecasts for a scalar random variable. In this paper it is shown how the optimal combination parameters can be obtained with the help of linear regression. Thus numerical considerations as well as application of linear plus quadratic combination to empirical data are facilitated. First results on the comparison of the new methods to the classical linear approaches are given. It is found that there are situations where the linear plus quadratic approaches may be employed beneficially, but further investigations have to be carried out.