More Formal Definition
A time series is mean-reverting if its returns have negative autocorrelation.
Under this definition a below-average return in one period is compensated for by a higher-than-average return in subsequent periods. The VIX is mean-reverting under this definition. It has a daily autocorrelation of -0.04, weekly of -0.21, and monthly of -0.12. This model can be simply expressed as
where
R are the returns at time t p is the autocorrelation fi is the mean return a is the volatility of the returns
Z is a draw from a standard normal distribution
A realization of this process is given in Figure 3.6. Now contrast this with Figure 3.7.
This is not proof of anything. But it is certainly suggestive that this form of mean reversion is applicable to the VIX, at least for short periods.
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