Seasonal AR(2) and AR(6) models rarely reproduced six-month Nino 3.4 change asymmetry in 1950-2025

We tested whether seasonal linear models reproduce a previously selected six-month cubic change statistic in a fixed NOAA ERSSTv5 Nino 3.4 record for 1950-2025. The observed statistic was -0.5066. In 1,999 records from a fitted month-specific AR(2) model with independent Gaussian noise, 10 had an absolute statistic at least this large. The nominal tail fraction was 0.0055. A stationary control and seasonal AR(2) and AR(6) checks with Gaussian or empirical noise gave fractions from 0.0010 to 0.0095. The models did not fully reproduce the observed two-year correlation. This result is conditional on fixed fitted parameters and independent additive noise. It does not reject all seasonal linear models or establish a physical cause. Prior statistic selection, data reuse, source reconstruction error and model mismatch limit inference. Code, exact source hashes, scalar simulation evidence, a figure and an internal numerical audit are included. Monthly source and derived records remain external.

ENSO · Nino 3.4 · seasonal autoregression · model check · change asymmetry · conditional inference