The statistical significance of multivariate Hawkes processes fitted to limit order book data

Understand

Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems.

• Given a calibrated Hawkes process, of concern is the statistical fit to empirical data, particularly for the accurate quantification of self- and mutual-excitation effects.
• We investigate the application of a multivariate Hawkes process with a sum-of-exponentials kernel and piecewise-linear exogeneity factors, fitted to liquidity demand and replenishment events extracted from limit order book data.
• We consider one-, two- and three-exponential kernels, applying various tests to ascertain goodness-of-fit and stationarity of residuals, as well as stability of the calibration procedure.