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 figures 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. Note that the VIX has followed our predicted trajectory
issued last month quite well, and is expected to bottom around
the end of the next quarter/the beginning of the last quarter of
2003.
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