More interim results on the Universal ENSO Proxy (UEP) DiffEq fitting.

1. The RHS forcing is getting closer to the QBO modulation as per #32. This 2.673 rads/yr (highlighted in yellow) is very close to the mean QBO period of 28 months
2. I added a slight modulation term to the LHS non-linear Mathieu sin() factor
3. For the other RHS forcing, I modulated the 6.2-year period (yellow highlighted 1 rads/yr) slightly as well. I am calling this a Chandler Wobble beat factor because that is what it is closest to in value.
4. (edit) I also filtered out a slight low-freq background modulation to see if that would help locking in, see the first line in figure below.

The correlation coefficient is almost 0.42

Recall that this is a 300+ year time-series and the coefficients are very close to those used in the SOI fit covering only the last century -- see [Figure 2 here](). So the ENSO years 1650 to 1900 revealed by proxy have a similar structure to the non-proxy results of post-1900, as far as the best-fit DiffEq structure is concerned.

I am becoming more confident that this DiffEq structure describes a significant underlying pattern in the dynamics of ENSO and the trail is leading us closer to unraveling one important piece of the puzzle.

![UEP](http://imageshack.com/a/img674/8254/qLzzV0.gif)


I was also thinking this is a good example of the training set/test set approach described in the latest blog post by David Tweed. The training set could be the ENSO SOI, and the test set the ENSO Proxy data. Or vice versa.

Comments encouraged, as Feynman warned that it is most easy to fool oneself.

thanks, Paul Pukite