Nonlinear Local Dependence Analysis with Application to Stock Price Changes and Volume

This paper proposes a new approach for local dependence analysis which exploits relationships at less frequent situations: a population version of contingency table analysis of two distributions expressed in a colored figure, and local impulse response analysis. The local dependence is measured by mutual information computed based on bivariate nonparametric density estimates with additional devices for improving accuracy. The significance of the estimate is assessed by comparing with the null confidence band which is obtained by bootstrap method. The application example is presented with respect to dynamic relationship between the daily NYSE index returns and volume from 1965 to 2008, where the following empirical regularities are found: (1) The effect of negative past returns to the volume in the same and the next day is in the opposite direction depending on the size of the downfall; (2) Large price downfall weakly induces persisting low volume, while large price increase significantly induces large volume which disappears in a shorter period; (3) While the impact of price changes is symmetric just after the shock, the effect of large price increase disappears in one or two days, but the effect of large price decrease persists; (4) High past volume induces high positive returns for several days.