Regression analysis for periodic data

#1
I am working on a hedging model for commodity.I have past 36 months data of commodity market price and future contracts price.
e.g. on 1st April,2014, market price is x,April contract price = x+1,May contract price = x+2 and June contract price = x+2
I have to find pattern between market price and contract prices. I am testing data with multiple regression so that I can put all variables in equation.
Say,we get three different equations and coefficient for April 2013,April 2014 and April 2015 data.Since I have to find out single pattern for April,what should I do?Can I take mean of coefficients? At the end, I am planning to write a matrix which will have coefficients for each month and I am assuming it would help me to forecast prices based on past data.
Please let me know if my approach is wrong.Also feel free to suggest any other approach.Thanks for reading:)