Petrozavodsk State University

Deciding whether an auxiliary time series genuinely improves prediction of a target has relied mainly on error-magnitude measures such as RMSE or Granger gain. The new construction takes matched target-only and target-plus-source multi-horizon forecasts, computes Shannon entropy of the signed forecast-error distribution at each horizon, and turns the change of that entropy profile across horizons into a directed descriptor. Across four equal-power hidden nonlinear channels the noise-averaged response-sensitivity statistic is 29.00, 27.47, 23.22 and 28.67, versus 14.09, 10.68, 12.67 and 12.71 for mean log-RMSE gain, and the response stays positive in all 108 tested combinations of window length, history length and maximum forecast horizon.

Deciding whether an auxiliary time series genuinely improves prediction of a target has relied mainly on error-magnitude measures such as RMSE or Granger gain. The new construction takes matched target-only and target-plus-source multi-horizon forecasts, computes Shannon entropy of the signed forecast-error distribution at each horizon, and turns the change of that entropy profile across horizons into a directed descriptor. Across four equal-power hidden nonlinear channels the noise-averaged response-sensitivity statistic is 29.00, 27.47, 23.22 and 28.67, versus 14.09, 10.68, 12.67 and 12.71 for mean log-RMSE gain, and the response stays positive in all 108 tested combinations of window length, history length and maximum forecast horizon.