Imagine an economy in which we have stocks S1, S2, S3 and S4. These are common stocks and pay dividends etc. There is also a market cap weighted index I (weighted sum of S1 through S4).The stocks and I also have futures F1, F2, F3, F4 and F that also trade in this market.1) Claim 1 - The no arbitrage price of the Future F equals the market cap weighted prices of F1, F2, F3, F4 - I think this should be true but not 100% sure.Now I want to study divergences between F and F1,F2,F3,F4 and devise say a stat arb strategy - that basically trades when it sees a meaningful price divergence between a synthetic index of F1, F2, F3, F4 and F. What are the potential approaches. Does cointegration make sense? How about PCA? If I incorporate all futures in the study I may never get a signal. Lets say that the weight on the F1 and F2 add up to more than 80%, should I just trade a basket of F1,F2 and F as per their cointegrating vector, and study its properties.I may be nebulous here, but I am just trying to see if anyone else had generic ideas to approach this problem. Many thanks.