Another substantiation that ENSO is not chaotic. The scientists at NOAA filter out the annualized signal from the ENSO NINO34 index. Below is the part of the time series that they remove, labelled "ClimAdjust"
One can assert this is just a remnant of the well-known annual signal, but it is actually pulse-shaped and close to what I apply to modulate the tidal-signal to create a "spring-barrier" forcing that carries on to the next year.
What NOAA did was not proper signal processing. One shouldn't remove what may be considered nuisance parameters in a time-series by assuming that they relate to known (in this case seasonal) factors and so can be safely filtered out and ignored. In fact, that may be safe only **IF** those factors form an independent process and so don't cause non-linear interactions with the rest of the data. So if a model predicts a linear component and a non-linear component, it's not helping to hide the linear portion from the analysis. But that's not the only problem, as the filtering is over-zealous in that it removes all annual harmonics as well. Worse yet, the weighting of these harmonics changes over time, which means that they are removing other parts of the spectrum not related to the annual signal. This is all found in an "ensostuff" subdirectory: