Add an ACD arrival law
Table of Contents
This page is a capture in the inbox bucket of the product backlog — a pre-sprint idea, not yet pulled into a sprint as a story.
1. What
A fourth arrival law beside periodic, Poisson and Hawkes: Engle and Russell's
ACD(1,1). The expected gap is psi_i = omega + alpha * gap_(i-1) + beta * psi_(i-1),
and a gap is psi_i times a unit-mean draw. It is a value with visible state, as
the other laws are, drawn from the series' keyed stream, and it is stable while
alpha + beta < 1.
2. Why
Gemini's review offered it in a model selector. Hawkes clusters arrivals by exciting an intensity; ACD clusters them by making a short gap likely to follow a short gap. Trade durations are the data ACD was written for, and they are what a desk would calibrate a feed to. It costs one law, its validation, its column on the feed's Arrivals tab, and its compensator for the fit tests.
3. References
- Gemini's review of the Market regime tab
- Tick arrival
- Engle and Russell (1998), "Autoregressive conditional duration", Econometrica 66(5).
4. See also
- Carry a market-wide arrival regime — the story that built the market these extend.