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We introduce a novel modeling framework-the Hawkes(p, q) process-which allows us to parsimoniously disentangle and quantify the time-varying share of high frequency financial price changes that are due to endogenous feedback processes and not exogenous impulses. We show how both flexible exogenous arrival intensities, as well as a time-dependent feedback parameter can be estimated in a structural manner using an Expectation Maximization algorithm. We use this approach to investigate potential characteristic signatures of anomalous market regimes in the vicinity of 'flash crashes'-events where prices exhibit highly irregular and cascading dynamics. Our study covers some of the most liquid electronic financial markets, in particular equity and bond futures, foreign exchange and cryptocurrencies. Systematically balancing the degrees of freedom of both exogenously driving processes and endogenous feedback variation using information criteria, we show that the dynamics around such events are not universal, highlighting the usefulness of our approach: (i) post-mortem, for developing remedies and better future processes-e.g. improving circuit breakers or latency floor designs-and potentially (ii) ex-ante, for short-term forecasts in the case of endogenously driven events. Finally, we test our proposed model against a process with refined treatment of exogenous clustering dynamics in the spirit of the recently proposed autoregressive moving-average (ARMA) point process.

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