Duration Dependence in Bull and Bear Stock Markets

Testing duration in stock markets concerns the ability to predict the turning points of bull and bear cycles. The Weibull renewal process has been used in previous studies to analyze duration dependence in economic and financial cycles. A goodness-of-fit test, however, shows that this model does not fit data from U.S. stock market cycles. As a solution, this study fits the modulated power law process that relies on less restrictive assumptions. Moreover, it measures both the long term properties of bull and bear markets, such as the tendency of the cycles to become shorter (or longer), as well as the short term effects, such as duration dependence. The results give evidence of negative duration dependence in all samples of bull markets and evidence of positive duration dependence in complete, peacetime and post WWII samples of bear markets. There is no evidence of any structural change in duration dependence after WWII in either bull or bear markets. The results show that bull and bear markets tend to get progressively shorter, but for bull markets this trend has accelerated since WWII whereas for bear markets this trend has decelerated since WWII. Goodness-of-fit tests suggest that the modulated power is a suitable model for U.S. stock market cycles.