A previous monthly state cut six-month ENSO forecast error by 7.82% in a constant-coefficient model at 2000-2024 origins

We tested whether one previous monthly state improves a two-state ENSO forecast that already uses Nino 3.4 temperature and basin warm water volume. We used frozen NOAA GODAS and ERSSTv5 records, expanding fits from 1980, and 300 monthly origins in 2000-2024. In the constant-coefficient model, adding the previous state reduced six-month temperature mean squared error by 7.82%. RMSE fell from 0.7502 to 0.7203 C. The conditional 95% three-year block interval for error reduction was 1.30% to 14.10%. With seasonal intercepts and current-state slopes in both models, the gain was 3.34%, with limits of -3.30% to 8.43%. Five-year blocks gave the same distinction. The extra lag helps the simple constant model, but its added value beyond seasonal dynamics remains uncertain. This extends earlier temperature-history methods to a small model with subsurface volume. Revised inputs, few ENSO cycles, model choice and conditional intervals limit inference. The result does not identify physical memory or operational skill. Code, input hashes, aggregate scores, all score draws, a numerical audit and a figure are included.

ENSO · warm water volume · autoregression · memory · seasonal dynamics · chronological forecast