Monitoring Forecasting Combinations with Semiparametric Regression Models

In this study, a modelling framework is proposed for evaluating the accuracy of forecasting combinations when the number of available forecasts is large and changes in time. Squared forecast errors are modelled with a semiparametric additive regression model where the linear part involves indicator variables reflecting the time period when the forecast is performed and the nonparametric part involves a smooth function of the number of individual forecasts entering the combinations. The partial regression estimates permit two-dimensional plots of the relationship between squared forecast errors and the number of forecasts entering the combinations and can be used to assess the contribution of additional forecasts in reducing the forecast errors. The method is demonstrated with six empirical applications using macroeconomic forecasts published by Her Majesty’s Treasury.