State-dependent Hawkes processes and their application to limit order book modelling

We study statistical aspects of state-dependent Hawkes processes, which are an extension processes where a self- and cross-exciting counting process state fully coupled, interacting with each other. The excitation kernel the depends on that, reciprocally, switches when there is event in process. first establish existence uniqueness explain how they can be simulated. Then we develop maximum likelihood estimation methodology for parametric specifications apply to high-frequency limit order book data, allowing us build novel model that captures feedback loop between flow shape book. estimate two model, using bid–ask spread queue imbalance as variables, find effects strongly state-dependent. Additionally, endogeneity flow, measured by magnitude excitation, also state-dependent, being more pronounced disequilibrium states