A new testable implication is derived from the rational speculative bubbles model stating that the presence of bubbles implies positive duration dependence in runs of high returns. Specifically, the probability of observing an end to a run of high returns declines with the length of the run. Traditional duration dependence tests are adapted for use with discrete stock runs data and, consistent with the existence of bubbles, evidence of duration dependence in monthly real stock returns is found.

ABSTRACT This paper uses a Markov chain model to test the random walk hypothesis of stock prices. Given a time series of returns, a Markov chain is defined by letting one state represent high returns and the other represent low returns. The random walk hypothesis restricts the transition probabilities of the Markov chain to be equal irrespective of the prior years. Annual real returns are shown to exhibit significant nonrandom walk behavior in the sense that low (high) returns tend to follow runs of high (low) returns in the postwar period.

ABSTRACT We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross‐autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross‐sectional tests of the delay for individual securities suggest that existing explanations of the cross‐autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time‐varying risk premiums fail to capture the directional asymmetry in the data.

We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross-autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross-sectional tests of the delay for individual securities suggest that existing explanations of the cross-autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time-varying risk premiums fail to capture the directional asymmetry in the data.