ARMAX models explaining the annual variations in Downs herring spawning midpoint, start, ending and duration in relation to autoregressive (AR) and moving average (MA) factors, as well as external variables at different time lags shown in brackets (<i>SSTAw</i> = annual sea surface temperature anomaly on wintering spawning grounds, <i>CALf</i> = annual changes in the abundance of <i>Calanus finmarchicus</i>; <i>CALh</i> = annual changes in the abundance of <i>Calanus helgolandicus</i>).

All the explanatory variables significantly (p < 0.05) cross-correlated to the phenological metrics are reported in the “External variables” column, although only those retained in the final model are shown in the “Final ARIMAX model” column.