Antithetic twins to cancel origin-linked forecast bias

Bias that stays tied to the base period

Autocorrelation in an ordered price series can bias a quantitative forecast, and that bias can depend on the forecast-origin. The forecast-origin is the most recent historical observation used as the base period of a projection; systematic forecast error can change with this point.

The described origin-linked-bias is not assumed to vanish as more history is added. The problem statement is that additional observations can leave the forecasts still biased and less reliable.

Serial-correlation is the dependence of ordered observations on their own earlier values, which breaks the independent-observation assumption of many statistical models. In the archive workflow the baseline is a spectral-time-series-model: a quantitative model that extracts cyclical structure from ordered price observations over a defined lookback and sampling interval.

Building the antithetic companion

Averaging two forecasts is presented as more informative when the components are not highly positively correlated, because each then contributes information the other does not already contain.

The antithetic construction raises each historical observation, and the baseline forecast, to a small fixed negative power, illustrated with -0.001, so the new series is negatively correlated with the original. The antithetic-companion is that reverse-correlated transform of the baseline series or forecast, built so origin-linked errors have opposite sign.

The antithetic values are mapped back to the original scale with a linear regression whose intercept and slope are estimated from the same historical window used to fit the baseline model.

The baseline in the illustration is a moving-window spectral-time-series-model fitted on 88 monthly closings of a broad industrial equity average and then projected over a 12-month horizon.

Holding combination weights fixed

Forecast-combination is a predetermined weighted blend of two component projections intended to cancel opposing errors instead of selecting one model.

Combination weights are chosen from known history to reduce squared fit error, or calibrated on a designated trial period when the inner model cannot be opened. Trial-period-calibration estimates those weights on a designated historical or holdout window, then holds them fixed for later periods.

All horizon points can be produced first and then combined, or combination can be applied sequentially so each combined value informs later forecasts.

The pairing procedure is presented as independent of the underlying forecasting model and as not requiring a specified error distribution, because the companion errors are constructed to be reverse correlated.