On the Variance of Antithetic Time Series

Abstract

Combining antithetic time series is used to reduce model fitted and forecast mean square error (MSE). This is accomplished by removing the component of error that represents bias. The potential to reduce error is a function of variance in the time series. The greater the variance the greater is the potential for error reduction. But, the greater the variance the less is the efficacy of reversing correlation and combining antithetic time series. The percentage reduction in MSE increases with variance up to a limit then reduces.