Although the historical coral proxy measurements are not high resolution (1 year resolution available), they can provide substantiation for models of the modern day instrumental record. This post is a revisit of a previous analysis of the Universal ENSO Proxy (UEP).
The interval from 1881 to 1950 of the ENSO data was used to train the DiffEq ENSO model. This gives a higher correlation coefficient (~0.85) on the test interval (from 1950 to 2014) than the training interval (1881-1950) as shown below:
Fig. 1: ENSO model fit over the modern instrumental record
Since ENSO data shows stationarity and coherence over the interval of 70 years, this fit was re-applied to the UEP data over 4 different ranges 1650-1720, 1720-1790, 1790-1860, and 1860-1930. High correlation coefficients were found for each of these intervals (> 0.70) and compared against fits to a red noise model shown below:
Fig 2: Proxy fits over various ranges as compared to a red noise model (added for clarification: essentially a synthetic data set to evaluate the ENSO model against). The significance is at least at 0.95 for each proxy interval.
Each of the ENSO fits lies within the 0.95 significance level, and only 1 out of 500 red noise simulations obtained a 0.8 correlation coefficient, which is what the 1720-1790 interval achieved.
The significance of having each of these intervals at least 0.95 is 1-(1-0.95)^4 if these are all independent. That is a small number less than about (1/20)^4 in likelihood.
The caveat is that the ENSO is also not likely to be coherent over intervals much greater than 70 years, as the shift around 1980 in phase for the model demonstrates.
This substatntiates the finding of Hanson, Brier, Maul  that ENSO and El Nino frequencies may be relatively constant back to the year 1525.
Astudillo et al  also confirmed the ENSO shift after 1980 stating that "the amplitude of the 1982-1983 event is unique". Further they concisely describe the ENSO behavior as being highly deterministic by stating:
"This is of crucial importance since if a system is deterministic, the vector field at every period of the state space is uniquely defined by a set of ordinary differential equations."
 K. Hanson, G. W. Brier, and G. A. Maul, “Evidence of significant nonrandom behavior in the recurrence of strong El Niño between 1525 and 1988,” Geophysical Research Letters, vol. 16, no. 10, pp. 1181–1184, 1989.
 H. Astudillo, R. Abarca-del-Río, and F. Borotto, “Long-term potential nonlinear predictability of El Niño–La Niña events,” Climate Dynamics, pp. 1–11, 2016.