A semi-parametric point process model of the interactions between equity markets

A novel point process framework to examine the links between transaction data across equity markets is proposed. Moving beyond a simple exponential kernel specification, it is shown that the kernel matrix can be estimated by solving a system of integral equations which is uniquely characterised by second order cumulants. The cumulant based estimator is shown to be asymptotically normally distributed and consistent and is shown to perform well in a small simulation study. Applying this method to data from U.S and U.K. equity markets when both are open, reveals that two-way interaction between trades is significant. Moreover, this interaction is characterised by both complex short term dynamics and long memory, which cannot be captured by conventioanl exponential kernels.