Abstract
AbstractThree 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.
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