A considerable amount of papers use a cost-carry model in modelling the relationship between future and spot index prices. The cost-carry model defines basis, bt;T , at time t and maturity date of the future contract at T as bt;T = ft � st = r(T � t), where ft, st and r denote the log of future prices, the log of spot index prices and the difference between interest rate and dividend rate, respectively. Using daily data time series on future contracts of the S&P 500 index and the FTSE 100 index, as well as the price levels of the corresponding underlying cash indices over the sample period from January 1, 1988 to December 31, 1998,  argued that there is significant nonlinearity in the dynamics of the basis due to the existence of transaction costs or agents heterogeneity. They found that the basis follows a nonlinear stationary ESTAR (Exponential Smooth Transition Autoregressive) model. However, based on the study with the S&P 500 data series from January 1, 1998 to December 31, 2009, we conclude that there is no significant difference between a linear AR(p) model and a nonlinear STAR model in fitting the data.
Available at: http://works.bepress.com/cgulati/5/