This is remarkable. Using the spreadsheet linked in the last post, the figure below is a model of ENSO derived completely by a training fit over the interval 1900 to 1920, using the Nino3.4 data series and applying the precisely phased Draconic and Anomalistic long-period tidal cycles.
Fig. 1 : The ENSO model in red. The blue BG region is used for training of the lunar tidal amplitudes against the Nino3.4 data in green. That data is square root compacted to convert it to an equivalent velocity.
Not much more to say. There is a major disturbance starting in the mid-1980’s, but that is known from a Takens embedding analysis described in the first paper in this post.
GeoEnergy Math 
This is also remarkable. Whether one trains the model in the early 1900’s versus the turn of the 2000’s, the results are nearly identical.
The underlying time series is stationary against changes of behavior over time. This is no different than conventional tidal analysis. These relatively short intervals are sufficient to capture the full spectral content of the entire series.
It’s still possible that another undetected behavior rides alongside the model, or that noise plays some role.
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