2016/04/06 by Roger Martins, Dieter Hendricks, Martins, Roger +1
Mathematics · #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1604.01824
Hawkes processes have seen a number of applications in finance, due to their\nability to capture event clustering behaviour typically observed in financial\nsystems. Given a calibrated Hawkes process, of concern is the statistical fit\nto empirical data, particularly for the accurate quantification of self- and\nmutual-excitation effects. We investigate the application of a multivariate\nHawkes process with a sum-of-exponentials kernel and piecewise-linear\nexogeneity factors, fitted to liquidity demand and replenishment events\nextracted from limit order book data. We consider one-, two- and\nthree-exponential kernels, applying various tests to ascertain goodness-of-fit\nand stationarity of residuals, as well as stability of the calibration\nprocedure. In line with prior research, it is found that performance across all\ntests improves as the number of exponentials is increased, with a\nsum-of-three-exponentials yielding the best fit to the given set of coupled\npoint processes.\n