Regressing regression coefficients against other sets of data

Hi guys

A bit of a background. I am a trader by profession and have moderate knowledge of stats. I am building a model which prices a futures curve out about one year at any point in time. I started by using the dynamic Nelson and Siegel equation (so a trig function to fit my data) and added a fourth term to fit seasonality present in the prices. I ran least squares on the model and came out with 4 coefficients (R-squared was close to .99 most of the time) over a span of a few years. I then ran a correlation matrix with the four coefficients and a slew of fundamental data (production, consumption, weather, etc...) corresponding to each date. My hope was to find factors that influenced the 4 coefficients and run a regression on the coefficients to predict their values and then fit the coefficients back into the Nelson Siegel model to get a futures curve. I was surprised to see that not a lot of correlation (i think the max was around 0.70) was present and if there was, there was barely any logical link between the numbers.

My question(s) is(are): what am i doing wrong? i know there should be some sort of a link between the way the futures curve is shaped and the fundamental data i tried to correlate it my thinking here flawed? can i regress a least squares coefficient? or do i need to modify the data somehow?

Thanks in advance for the help guys
i havent really gotten to the point of regression, the first regression isnt really a regression but a least squares fit of a trig function...hence why i get coefficients from the least squares and test for correlation to fundamental data...of which i dont see any in order to run the second regression. does that make sense?