I'm currently calculating the Long Term/Short Term model of Schwartz and Smith to UK natural gas futures data. To save myself extra parameters when I run the Kalman filter I want to approximate the seasonality before I calibrate the other parameters.The SDEs are( Now the Chi term is meant to be a short-term OU process, mean-reverting to 0, whilst the Xi term is a long-term equilibrium price GBM. My current plan to get the seasonality was to use MATLAB's Curve Fitting Toolbox to fit a Fourier Series to historical monthly averages of the log spot price but I don't know how to get the December and January ends of the curve to line up. It would be a nightmare to have seasonality suddenly jump because Jan 1st suddenly rolls round.I have reliable data back to 2000 for the Day-Ahead (which I'm using as a proxy for the spot) and other Forwards.Any ideas about how to distangle a sensible curve for the seasonality function? Thanks in advance.

If you are using a Fourier over the course of the year, then they _will_ match up--it is a periodic function.Check out http://aede.osu.edu/people/roberts.628/ ... .Somewhere, I have a paper that occurs earlier than this one with an analytical solution to the problem, but I no longer have an e-version. LMK if you want it.Matt.