Daily futures price changes and non-linear dynamics

Alternative models of the distribution of daily futures returns are tested. Daily futures returns are not normal with most having fatter tails than a normal distribution. Most are also skewed. In addition returns are not independent and exhibit non-linear dynamics. Among the diffusion-jump, extended GARCH (generalized autoregressive conditional heteroskedastic) and deterministic chaos processes, the GARCH(1, 1) process with residuals following a Student distribution comes closest to fitting the data. This model reduces leptokurtosis and serial dependence considerably. But, Kolmogorov-Smirnov tests of fit reject the GARCH(1, 1)-t process for all cases. The standardized residuals are still leptokurtic and skewed, and the GARCH captures the non-linear dynamics in about half of the cases. Since non-linear dependence remains in some cases, deterministic chaos remains a possibility.