Application of Stein Rules to Combination Forecasting

We propose some Stein-rule combination forecasting methods that are designed to ameliorate the estimation risk inherent in making operational the variance–covariance method for constructing combination weights. By Monte Carlo simulation, it is shown that this amelioration can be substantial in many cases. Moreover, generalized Stein-rule combinations are proposed that offer the user the opportunity to enhance combination forecasting performance when shrinking the feasible variance–covariance weights toward a fortuitous shrinkage point. In an empirical exercise, the proposed Stein-rule combinations performed well relative to competing combination methods.