Tbe Review of Financial Studies /v 5 n 2 1992 price relationship.More recently,Huffman (1988)and Ketterer and Marcet (1989)examine trading volume and welfare issues in various economies comprised of heterogeneous infinitely lived agents facing limited trading opportunities [also,see Andersen (1991)].Existing models,however,do not confront the data in its full complexity and have not evolved sufficiently to guide the specification of an empirical model of daily stock market data.For instance,there seems to be no model with dynamically optimizing,heterogeneous agents that can jointly account for major stylized facts-serially correlated volatility, contemporaneous volume-volatility correlation,and excess kurtosis of price changes-each of which we discuss below. In this article,we undertake an empirical investigation of the dynamic interrelationships among price and volume movements on the stock market.Our work is motivated in part by the recent events on the stock market,which suggest that more can be learned about the market-and,in particular,about volatility-by studying prices in conjunction with volume,instead of prices alone.It is also moti- vated by an objective of providing a full set of stylized facts that theoretical work will ultimately have to confront.Because of the limitations of existing theory,the empirical work is not organized around the specification and testing of a particular model or class of models.Instead,the empirical effort is mainly data-based.We begin with an informal graphical look at the data and then proceed ulti- mately to the estimation and interpretation of a seminonparametric (SNP)model of the conditional joint density of market price changes and volume in Section 3. The investigation has four objectives:(i)to analyze the relation- ships between contemporaneous volume and volatility in an esti- mation context that explicitly accounts for conditional heteroskedas- ticity and other forms of conditional heterogeneity;(ii)to characterize the intertemporal relationships among prices,volatility,and volume; (iii)to examine the "leverage"effect,which is an asymmetry about the vertical axis in a plot of the conditional variance of current price change against past price change,and to examine the extent to which conditioning on past volume reduces or increases the asymmetry;and (iv)to determine what,if any,relationship there is between the conditional mean and variances of price changes. These objectives relate to features of the conditional density of the price change and volume data,and not to the signs and magnitudes of specific parameters.The conditional density is the fundamental statistical object of interest,as it embodies all of the information about the probabilistic structure of the data.Hence,as noted above,we employ a seminonparametric approach to estimate the density directly. 202