  This article presents a Hawkes process model with Markovian baseline
intensities for high-frequency order book data modeling. We classify intraday
order book trading events into a range of categories based on their order types
and the price changes after their arrivals. To capture the stimulating effects
between multiple types of order book events, we use the multivariate Hawkes
process to model the self- and mutually-exciting event arrivals. We also
integrate a Markovian baseline intensity into the event arrival dynamic, by
including the impacts of order book liquidity state and time factor to the
baseline intensity. A regression-based non-parametric estimation procedure is
adopted to estimate the model parameters in our Hawkes+Markovian model. To
eliminate redundant model parameters, LASSO regularization is incorporated in
the estimation procedure. Besides, model selection method based on Akaike
Information Criteria is applied to evaluate the effect of each part of the
proposed model. An implementation example based on real LOB data is provided.
Through the example, we study the empirical shapes of Hawkes excitement
functions, the effects of liquidity state as well as time factors, the LASSO
variable selection, and the explanatory power of Hawkes and Markovian elements
to the dynamics of the order book.
