Hawkes Processes

Some records breed their own events. An aftershock raises the chance of the next one, an infection causes the next infection, a price spike makes another more likely. The Hawkes process is the model of that, and one number, the branching ratio, decides whether a cascade dies out or runs away. Seismologists call it productivity, epidemiologists the reproduction number, bankers and insurers contagion, traders endogeneity.

This book fits that one model to five public records: the Ridgecrest aftershocks, the Delta wave of COVID-19, nine decades of bank failures, thirty years of hurricane losses and the Henry Hub gas price. It asks each the same question: does it really breed events? Fitted naively, all five say yes. Let the baseline move, or test against a common shock, and only some still do.

The main results are proved, every estimate is tested by its residuals and computed two ways, and the Python that draws every figure is printed in full.

Callum Whitlow is an applied probabilist from Wellington who has forecast aftershock rates, priced clustered catastrophe claims and estimated reproduction numbers.