The endo-exo problem in high frequency financial price fluctuations and rejecting criticality

The endo-exo problem lies at the heart of statistical identi fication in many fields of science, and is often plagued by spurious strong-and-long memory due to improper treatment of trends, shocks and shifts in the data. A class of models that has shown to be useful in discerning exogenous and endogenous activity is the Hawkes process. This class of point processes has enjoyed great recent popularity and rapid development within the quantitative fi nance literature, with particular focus on the study of market microstructure and high frequency price fluctuations. We show that there are important lessons from older fi elds like time series and econometrics that should also be applied in fi nancial point process modelling. In particular, we emphasize the importance of appropriately treating trends and shocks for the identi fication of the strength and length of memory in the system. We exploit the powerful Expectation Maximization (EM) algorithm and objective statistical criteria (BIC) to select the flexibility of the deterministic background intensity. With these methods, we strongly reject the hypothesis that the considered financial markets are critical at univariate and bivariate microstructural levels