Optimal antithetic weights for lognormal time series forecasting

The theory for estimating optimal weights for combining antithetic fitted values which contain antithetic (negatively correlated) errors, produced from lognormal historical time series, is presented. The functions which determine the optimal weights used to combine the lognormal and linear projection of the antithetic fitted values, are derived. The method reduces mean square fitted error (mse), when tested on simulated lognormal and non-lognormal autoregressive series of varying order. Antithetic forecasting yields reductions in forecast mse (which otherwise increases with forecast horizon), up to about 50% in large-scale empirical validation tests applied to 111 time series.