Combining Global Antithetic Forecasts

This paper provides a summary of the theory for antithetic forecasting, and an empirical exposition. An original forecast is combined with another forecast, produced from a time series which is antithetic (negatively correlated) to the original time series. The forecasts are combined via a linear projection of the antithetic series on the original series, such that the component forecasts have negatively correlated errors. Large-scale empirical tests and benchmark comparisons demonstrate the effectiveness of combining antithetic forecasts, even as these data depart from the strict theoretical lognormality requirement of antithetic forecasting. The method is illustrated in detail, using a real time series. Antithetic forecasting is the first combining method in which the gain increases with the forecast horizon.