A Bivariate Generalized Autoregressive Conditional Heteroscedasticity-in-Mean Study of the Relationship between Return Variability and Trading Volume in International Futures Markets

Abstract

The relationship between trading volume and price changes in futures markets continues to be of interest mainly due to the inconclusive nature of the results reported so far in the literature (Karpoff, 1987). One source of controversy centers on the empirical distribution of futures price changes (Sterge, 1989).A recent study by Najand and Yung (1991) concludes that price changes in U.S. Treasury bond futures markets are best characterized by a time series model that allows for generalized autocorrelation as well as conditional heteroscedasticity (GARCH) in the second moments. Using this GARCH framework, Najand and Yung (1991) document a positive relationship between price variability and trading volume, consistent with both the mixture of distributions hypothesis (Clark, 1973), several se-quential equilibrium models of speculative markets (Copeland, 1976), and certain newer classes of noisy rational expectations equilibria (Blume, Easley, and O'Hara, 1994; Easley, Keifer, and O'Hara, 1994). This paper extends Najand and Yung's (1991) study in two ways. First, a cross-section of international futures markets is examined. A study of international futures markets is important because it provides independent verification of the results obtained in domestic markets. Second, a bivariate exponential GARCH(1,1)-in-mean model is used. In ad-dition to allowing for autocorrelation in the first and second moments, this model has the advantages of avoiding simultaneity bias with regard to the effect of volume on price volatility, allowing for nonlinearities in the second moments, as well as providing a means for estimating a risk premium.