Couple of questions:

(1) Why use of second (I presume time) derivative of the ENSO? And that's related to ...
(2) What's the form of the design matrix used in the regression, sometimes also called the factors matrix? It would have rows corresponding to observations and columns corresponding to things like _q1s_ and _q1c_.
(3) Can I get a copy of the raw design matrix and responses used for the fit? It would be good to have the raw _q1_, _s9_, _sd_, etc. Are these normalized in some way so it makes sense to extract the trigonometric projections?
(4) Regarding "(3)", if these are of lags, how's coincidence (zero lag) determined?

A quick look at the literature (mind, I'm no meteorologist or geophysicist or climatologist) indicates a _lot_ of work on connections between QBO and ENSO, e.g., (I don't have a copy because I don't subscribe) and its figures [1](, then [2](, then [3](, then [4](, then [5](, and the paper [6]( from the famous team of Gray, Sheaffer, and Knaff from 1992. So, I woudn't be surprised if there's a link. Is the link stronger than you suspected, or people suspect?