Separate warm and cold ENSO slopes gave no clear winter PDO forecast gain in 1981-2025

We tested whether separate warm and cold ENSO slopes improve winter PDO forecasts beyond recent PDO and linear Nino 3.4. We used fixed NOAA ERSSTv5 tables and 45 chronological tests in 1981-2025. Adding absolute Nino 3.4 raised winter mean squared error from 0.572125 to 0.575573, an increase of 0.60%. The conditional 95% five-year block interval for error reduction was -10.39% to +11.78%. Rolling fits, a time trend and a squared Nino term also gave no clear gain. Summer primary error rose by 4.44%. This extends prior campaign linear tests with one asymmetric response term. It does not establish that the physical response is symmetric. Short dependent records, revised shared-source indices, a selected simple model and uncertainty conditional on saved forecasts limit inference. The package includes exact inputs, hashes, code, all forecasts, block draws, a figure and a separate numerical audit.

PDO · ENSO · asymmetric response · seasonal forecast · null result · chronological validation