The enduring and existential problem with modeling of climate is that we never have a controlled experiment to evaluate our scientific theories against. We can interpret the model against recent instrumental data, but this is often not good enough for the skeptics that claim that it is 5-parameter elephant fitting.
So what is often done is to search for other data, such as selecting from what is available from historical proxy records. This can provide extra dimensions of the sample space for verifying results that were essentially trained and fit to recent data only.
For the SOI data, we have modern day instrumental data that goes back to about 1866. However, impressive historical proxy results have been unearthed by Cobb through an analysis of coral oxygen levels. After calibration of recent coral growth to modern equatorial sea-surface temperature (SST) records, the correlation is expected to sustain back through history. This makes it an adequate proxy representation for the Southern Oscillation Index (SOI) that we have been using to understand and potentially predict ENSO dynamics.
The verification experiment is to take several sets of coral measurements and determine if the same general Mathieu-equation fit that was used to model the SOI data could be applied universally. The answer is yes, the SOIM essentially uses similar parameters for the 12th, 14th, and 17th century ENSO proxy data.