Causality between Returns and Traded Volumes

This paper examines causality between the series of returns and transaction volumes in high frequency data. The dynamics of both series is restricted to transitions between a finite number of states. Depending on the state selection criteria, this approach approximates the dynamics of varying market regimes, or in a broader sense reflects the time varying heterogeneity of traders behavior. Our analysis is based on returns and volumes represented by chains with constant or time varying transition probabilities. The univariate return series is examined to identify varying market regimes and determine the impact of state specification on temporal dependence. In the bivariate framework we investigate co-movements between volumes and transaction prices, and propose tests for Granger causality. The trade size threshold yielding a dichotomous process featuring maximum volume-price causality is proposed as a volume classification criterion. We apply our methods to the Alcatel stock data recorded in real and calendar time, and discuss implications of the sampling frequency.