Nonlinear Dynamics and the Distribution of Daily Stock Index Returns

Three alternative models of daily stock index returns are considered: (1) a diffusion‐jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non‐nested tests between the diffusion‐jump process and a GARCH(1.1) process with t ‐distributed errors reject the diffusion‐jump process, but do not always reject the GARCH process. Kolmogorov‐Smirnov tests of fit, however, reject the GARCH(1,1)‐ t process for all cases. Nonlinear dependence is not removed for the value‐weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.