The following analysis is an excellent substantiation of the ENSO model
The fit does a back-extrapolation over a 230 year interval prior to 1880 using coral proxy records with a resolution of 1 year. The temporal forcing pattern is very close to that used in the modern record but the scaling has to be modified, as it appears that the magnitude of ENSO excursions were measurably reduced prior to 1880.
The salient point is that trying to fit a curve as chaotic-*appearing* as an ENSO time-series record by applying only 4 interacting sinusoidal waves is difficult enough. But then to extend that to almost double the length -- from 135 years to an additional 230 years with what are essentially minor tweaks to the boundary conditions -- is next to impossible if it was a truly chaotic behavior.