Testing of Dependencies between Stock Returns and Trading Volume by High Frequency Data

This paper is concerned with a dependence analysis of returns, return volatility and trading volume for five companies listed on the Vienna Stock Exchange and five from theWarsaw Stock Exchange. Taking into account high frequency data for these companies, tests based on a comparison of Bernstein copula densities using the Hellinger distance were conducted. The paper presents some patterns of causal and other relationships between stock returns, realized volatility and expected and unexpected trading volume. There is a linear causality running from realized volatility to expected trading volume, and a lack of nonlinear dependence in the opposite direction. The authors detected strong linear and nonlinear causality from stock returns to expected trading volume. They did not find causality running in the opposite direction. In addition, the existence of fractional cointegration was examined. Despite the equality of the long memory parameters of realized volatility and trading volumes, they do not move together in the long term horizon.