Stock Return Series Research Articles

A Reexamination of Finite- and Infinite-Variance Distributions as Models of Daily Stock Returns

This study investigates the general (asymmetric) stable Paretian distribution and three finite- variance, time-independent distributions applied to daily stock-return series. Previous empirical comparisons have, in general, ignored the existence and effects of skewness on the process parameters of stable laws. The results of log-likelihood ratio and log-odds tests indicate that finite-variance models still dominate after accounting for documented skewness. In particular, the mixed diffusion-jump and compound normal models appear to be the most descriptive time-independent models.

Long-term dependence in common stock returns

The efficient market, martingale model of security price movements requires that the arrival of new information be promptly arbitraged away. A necessary and sufficient condition for the existence of an arbitraged price is that statistical dependence among prices must decrease very rapidly. If persistent statistical dependence is present, the arbitraged price changes do not follow a martingale and should have an infinite variance. Using a technique for detecting long-term dependence, called R/S analysis, 200 daily stock return series are studied; many series are characterized by long-term dependence. Thus, in the presence of long-term dependence, the martingale model does not hold. Also, the distribution of security returns is non-normal stable Paretian as opposed to Gaussian.