This is the last of the ENSO charts.
This is how conventional tidal prediction is done:
This is an ENSO model fit to SOI data. Same tidal analysis algorithm is used but applying the annual solar cycle and monthly/fortnightly lunar cycles instead of the diurnal and semi-diurnal cycle.
This is an expanded view, with the corelation coefficient of 0.73:
This is a fit trained on the 1880-1950 interval (CC=0.76) and cross-validated on the post-1950 data
This is a fit trained on the post-1950 interval (CC=0.77) and cross-validated on the 1880-1950 data
Like conventional tidal prediction, very little overfitting is observed. Most of what is considered noise in the SOI data is actually the tidal forcing signal.