Fig. 7 analyses the VIX index by fitting it with our simple log-periodic formula. The VIX index is one of the world's most popular measures of investors' expectations about future stock market volatility (that is, risk). See http://www.cboe.com/micro/vixvxn/introduction.asp. For historical data, see http://www.cboe.com/micro/vixvxn/specifications.asp. The VIX time series is shown as the red wiggly curve. We have followed the same procedure as for Figs. 4-6: (i) we fit the real VIX data with our simple log-periodic formula; (ii) we then generate 10 synthetic time series by adding GARCH noise to the fit; (iii) we redo a fit of each of the 10 synthetic time series by the simple log-periodic formula and thus obtain the bundle of 10 predictions shown as the magenta lines. Strikingly, we first observe that our log-periodic formula is able to account quite well for the behavior of the VIX index, strengthening the evidence that the market is presently in a strong herding (anti-bubble) phase. Note also the rather good stability of the predictions, suggesting a reasonable reliability. |