The ENSO model is essentially two known (monthly) tidal parameters and one (annual) solar parameter provided as a RHS forcing to a primitive differential equation with LHS parameters that are roughly estimated.

Once these 5 LHS parameters are estimated from trial-and-error experiments shat show the greatest stationarity over the entire interval, the magnitudes and phases of the RHS parameters are discovered by fitting to any interval within the ENSO time series


That is a essentially an extreme over-fit to the interval covering the range 1900 to 1920. Normally this amount of over-fitting will not extrapolate well, yet this does. The model probably will end up working as well as any conventional tidal analysis, especially considering the maturity of this model.