Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets

This paper studies time-series dependence in the direction of stock prices by modelling the (instantaneous) probability that a bull or bear market terminates as a function of its age and a set of underlying state variables such as interest rates. A random walk model is rejected both for bull and bear markets. Although it fits the data better, a GARCH model is also found to be inconsistent with the very long bull markets observed in the data. The strongest effect of increasing interest rates is found to be a lower bear market hazard rate and hence a higher chance of continued declines in stock prices.