Neural Hawkes Processes for Event Sequences

A classic Hawkes process models order-flow events — trades, order arrivals, cancellations — as self-exciting: one event temporarily raises the odds of another happening soon after, with the effect decaying over time in a fixed exponential shape. That's a good first approximation of clustering in market activity, but it assumes every event type excites every other in the same simple decaying way, and real order flow is messier than that — a large aggressive trade might excite same-side momentum for a while, then trigger an entirely different pattern of liquidity replenishment a few seconds later, with a shape no single exponential curve captures well.

A neural Hawkes process replaces the fixed exponential-decay formula with a neural network (typically a recurrent network) that reads the history of past events and outputs a flexible, learned intensity — the instantaneous rate at which the next event of each type is expected — that can rise, fall, and even oscillate in ways a hand-specified formula can't. Instead of assuming a functional form and fitting a handful of parameters, the model learns directly from data what the excitation pattern actually looks like for each combination of event types.

In an order-flow setting, this means the model can learn, for example, that a large sell trade sharply raises the near-term probability of more sell trades for the next second or two, then that effect fades, but simultaneously raises the probability of a resting buy order appearing a bit further out as liquidity providers refresh their quotes — two different learned patterns for two different downstream event types, coexisting in the same model, something a single shared decay parameter cannot represent.

What this means in practice

Neural Hawkes models are used to forecast short-horizon order-flow intensity for execution algorithms (when is the next burst of activity likely, and in which direction) and to build more realistic order-flow simulators than a plain Hawkes process allows. The cost is the usual one for swapping a simple parametric model for a neural one: more data is needed to fit it reliably, and it's harder to explain to a risk committee why the model predicts what it predicts, compared to pointing at a single decay-rate parameter.