> Note that since this index is defined in terms of sea surface temperatures, we can think of the challenge this way: use current sea surface temperatures to predict aspects of future sea surface temperatures. Of course there’s no need to restrict ourselves to using current sea surface temperatures - we could use the Dow Jones industrial average if that helped. But using just sea surface temperatures makes it into an interesting self-contained game: “how much do sea surface temperatures now know about future sea surface temperatures”?
See the [publications of Tim DelSole](ftp://cola.gmu.edu/pub/delsole/webpage/publications.html) for some literature on the predictability of sea surface temperature; his "predictable component analysis" may be of some interest. You may also be interested in [this review paper on ENSO predictability](http://www.gfdl.noaa.gov/bibliography/related_files/avf0301.pdf) and [this paper on information-theoretic measures of ENSO predictability](http://onlinelibrary.wiley.com/doi/10.1029/2011JC007249/abstract). There is a fairly substantial literature on this subject applied to the predictability of particular modes of SST variability, not just ENSO.