Transaction Data Tests of the Mixture of Distributions Hypothesis

Abstract

This paper presents new tests of the mixture of distributions hypothesis. Previous tests examined security prices and volume measured only at daily intervals. Here, differential implications ofthe hypothesis for transaction data are derived and tested. The new predic? tions emanate from the assumption that prices and volume evolve at uniform rates in trans? action time. The results support this assumption and the mixture of distributions hypothe? sis in general. In addition, the tests suggest that the daily transaction-count may be a useful instrumental variable for estimating unobserved realizations of stochastic price variances. I. Introduction Clark [3] proposes that a mixture of normal distributions be used to model the distribution of daily security price changes. His model assumes that events important to the pricing of a security occur at a random, not uniform, rate through time. Using the same assumption, Harris [6] and Tauchen and Pitts [11] show that the joint distribution of daily price changes and volume also can be modeled by a mixture of bivariate normal distributions. Empirical implications of a random rate of flow of information (the mixture of distributions hypothesis) for the distributions of daily price changes and vol? ume are examined in detail by Clark [3], Morgan [9], Westerfield [12], Harris [6], [7], Tauchen and Pitts [11], and others. They show that the hypothesis can explain why the distribution of daily price changes is kurtotic relative to the nor? mal distribution, why the distribution of the daily volume of trade is positively skewed, and why squared (or absolute) daily price changes are positively corre? lated with trading volume. These predictions are all confirmed in studies of daily data. Although the empirical results in these studies strongly support the mixture hypothesis, they are subject to criticism. It may be that the above-mentioned properties of the daily data are simply a consequence of similar properties found