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 process of Hawkes branching ratio estimation, proposed as a proxy for market endogeneity in recent publications and formerly estimated using numerical maximisation of likelihood . We employ this 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.
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.
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