A set of 180 high quality stock titles is analyzed on hourly and daily time scale for conditional heteroskedastic behavior of individual volatility, further accompanied by bivariate GARCH(1,1) regression with index volatility over the three-year period of 2000/7/4 to 2003/6/30. Persistence of individual prices with respect to randomly chosen initial values (individual persistence) is compared to the collective persistence of the entire set of data series, which exhibits stylized polynomial behavior with exponent of about -0.43. Several modified approaches to quantifying individual and index-wide persistence are also sketched. The inverted fat tail series of standard persistence are found to be a useful predictor of substantial inversions of index trend, when these are used to compute the moving averages in a time window sized 200 steps. This fact is also emphasized by an empirical evidence of possible utilization in hedging strategies.
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