Combining Negatively Correlated Forecasts
by Denis Ridley, Ph.D.
Will combining two negatively correlated forecasts of price data produce a more accurate forecast?
STOCKS & COMMODITIES contributor Denis Ridley says yes. It's called "antithetic forecasting", as he
Traders and investors may find that forecasting models are useful for estimating future values of a
financial time series. However, serial correlation creates a biased forecast, and that bias in turn is
correlated with the forecast origin. Antithetic—or contradictory error—forecasting creates a new but
reverse correlated forecast and combines it with the original forecast, thereby canceling out the errors.
This article will illustrate an application to the monthly closings of the Dow Jones Industrial Average
(DJIA) in which the forecast mean square error was reduced by approximately 50% .
Antithetic forecasting falls into the category of methods referred to as combining forecasts. The antithetic
forecasting method can be applied when the historical data is autocorrelated—that is, when the data is
correlated with itself in previous time periods.
Autocorrelation is the basis for assuming that a historical series contains a pattern. If that is the case, then
there should be a forecasting model that can emulate that pattern, thereby generating the desired
forecasts. At the same time, we are reminded (see J.F. Elder and M.T. Finn's work in the reference
section) that the financial markets are normally difficult to forecast, so every effort to reduce forecasting
error becomes important. Statistical models assume that historical data is a collection of independent