  This study analyses the duration dependence of events that trigger volatility
persistence in stock markets. Such events, in our context, are monthly spells
of contiguous price decline or negative returns for the S&P500 stock market
index over the last 145 years. Factors known to affect the duration of these
spells are the magnitude or intensity of the price decline, long-term interest
rates and economic recessions, among others. The result of interest is the
conditional probability of ending a spell of consecutive months over which
stock market returns remain negative. In this study, we rely on continuous time
survival models in order to investigate this question. Several specifications
were attempted, some of which under the proportional hazards assumption and
others under the accelerated failure time assumption. The best fit of the
various models endeavored was obtained for the log-normal distribution. This
distribution yields a non-monotonic hazard function that increases up to a
maximum and then decreases. The peak is achieved 2-3 months after the spells
onset with a hazard of around 0.9 or higher; this hazard then decays
asymptotically to zero. Spells duration increase during recessions, when
interest rate rises and when price declines are more intense. The main
conclusion is that short spells of negative returns appear to be mainly
frictional while long spells become structural and trigger hysteresis effects
after an initial period of adjustment. Although in line with our expectations,
these results may be of some importance for policy-makers.
