On the efficacy of constraints on the linear combination forecast model

Combination forecasting has been demonstrated to be a successful technique for enhanced forecast accuracy of economic and financial variables. An established method to generate the component-forecast weights is the ordinary-least-squares (OLS) regression technique: Actual values of a variable are regressed on within-sample values of forecasts generated by alternative forecast sources. The estimated regression coefficients then serve as weights for out-of-sample combination forecasts. The present study addresses the controversy regarding the efficacy of placing restrictions on the combining model when generating weights for out-of-sample forecasts. Combinations are formed of component earnings-growth forecasts generated separately by financial analysts and a statistical model. Both restricted and unrestricted OLS are used in turn to generate the component-forecast weights. The findings suggest that combinations formed with weights generated by OLS with the constant suppressed and the sum-of-the-coefficients constrained to equal one, lead to enhanced forecast-accuracy and generally perform best. This study differs from a previous related study appearing in Applied Financial Economics1 in at least three main ways: (1) Combination forecasts are formed using actual regression-coefficients as forecast weights; (2) Forecast weights are generated using unrestricted OLS, as well as restricted OLS; (3) All combination forecasts are strictly ex-ante simulated.