Nonlinear dynamics of daily cash prices

Daily cash price changes are not normally distributed. Their empirical distributions have fat tails and most are skewed. In addition, they are not independent. Among the diffusion-jump, extended generalized autoregressive conditional heteroskedasticity (GARCH), and deterministic chaos processes, a GARCH process with residuals following a student distribution is the most likely. Our GARCH model reduces leptokurtosis, removes nonlinear dependence, and provides a considerable improvement over the i.i.d. normal model. The GARCH process is not well calibrated because it cannot explain all the observed nonnormality, but it does yield asymptotically valid hypothesis tests.