Is There a Symmetric Nonlinear Causal Relationship between Large and Small Firms?

This paper uses both linear and nonlinear causality tests to reexamine the cross-autocorrelation between the returns on large and small firms. Consistent with previous results, we find that large firms lead small firms, but small firm autocorrelation, nonsynchronous trading, or a differential response to a large set of economy-wide information cannot explain this finding. More important, in contrast to the received literature, we find significant nonlinear causality that is bidirectional and of the same duration in either direction. After controlling for possible sources of nonlinearities, such as information flow as proxied by volatility, macroeconomic information, business cycle effects, and nonsynchronous trading, we continue to find strong evidence of equal duration, bi-directional nonlinear causality