PLANNED · research
Hypothesis
Trade arrivals cluster (one trade raises the probability of the next), modelled by a self-exciting Hawkes process. The fitted branching ratio may flag the build-up of a liquidation cascade before price confirms.
Math — Hawkes conditional intensity
Intensity rises with each past event and decays exponentially:
$$ \lambda(t) = \mu + \sum_{t_i < t} \alpha\, e^{-\beta (t - t_i)} $$
The branching ratio $n=\alpha/\beta$ measures endogeneity; $n\to1$ signals criticality.
Method
Plan: fit $\mu,\alpha,\beta$ online by MLE on the aggregate-trade stream per symbol; monitor $n=\alpha/\beta$ as an early-warning of self-reflexive flow. Not yet built.
Queued. Filan & Sornette-style endogeneity ($n\to1$) is a clean criticality measure; the open question is whether it leads price by enough to act on, net of cost. To be tested as a risk-off gate first, not an entry.
Self-exciting clustering is one of the few genuinely robust empirical facts about order flow. Whether it is predictive rather than merely descriptive is the whole question.