Branching ratio approximation for the self-exciting Hawkes process

Understand

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes.

• Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data.
• The method we propose greatly simplifies the estimation of the Hawkes branching ratio, recently proposed as a proxy for market endogeneity and formerly estimated using numerical likelihood maximisation.
• We employ our new method to support recent theoretical and experimental results indicating that the best fitting Hawkes model to describe S&P futures price changes is in fact critical (now and in the recent past) in light of the long memory of financial market activity.