Modelling the Limit Order Book with an Eight-Variate Hawkes Process
An eight-variate Hawkes process calibrated by maximum likelihood to a full day of Apple (AAPL) TAQ top-of-book data. The calibration reveals a strikingly stable near-critical spectral radius of 0.95 across the trading day, and a multitype Galton-Watson cluster decomposition showing that around 95% of top-of-book events are endogenously triggered rather than driven by outside information.