Persistence and discontinuity in the VIX dynamics

We estimate the two Mandelbrotian parameters (“dual forms of wild variability”), namely, long-range dependence (Joseph effect) and discontinuity or fat tails (Noah effect) for the VIX stock market volatility measure. We find the VIX scalar series to be characterized by strong dependence (with nonstationary but mean-reverting dynamics) and fat tails with a power-law asymptotic behavior in the upper tail. The temporal stability analysis shows that the recent financial crisis, in particular, the collapse of Lehman Brothers in September 2008 and its aftereffects, had a pronounced impact on the behavior of the Mandelbrotian parameters. The presence of these statistical features in the VIX dynamics sheds valuable insight into the underlying data generating process for the VIX.