Optimal weights for combining antithetic forecasts

Antithetic forecasting is a new global method of combining forecasts. A theory for estimating optimal weights for combining antithetic forecasts is presented. Antithetic time series are generated by a power transformation applied to the original series. The fitted values are combined via a linear projection of the original series on the antithetic series, such that the original and antithetic fitted values have negatively correlated errors. The functions which determine the optimal weights used to combine the original and antithetic fitted values are derived. The method always reduced the mean square fitted error, when tested on extensive variations of simulated time series.