Nonlinearity Matters : The Stock Price – Trading Volume Relation Revisited

We apply a practical two-step procedure to test for nonlinear information in the stock price - trading volume relation. The approach draws upon the concept of transfer entropy and allows us to identify the dominant direction of the information transfer, which constitutes an improvement over (non-)linear Granger causality tests. We apply the procedure to a sample of more than 400 constituents of the S&P 500 over an 18 years time period. The findings suggest a substantial amount of nonlinear information transfer across stocks after accounting for all linear correlation and volatility persistence in the bivariate system of calendar-adjusted log-returns and trading volume growth. For most stocks, information predominantly flows from returns to trading volume. Our results call into question the widespread practice of modelling this dynamic relation with linear models