Hawkes Processes in Finance: What the Review Covers
Can a Hawkes process distinguish clustered market activity from ordinary seasonality?
Fit event intensities with a declared kernel and baseline, then inspect residuals against a time-varying seasonal baseline. A stationary constant-baseline model can attribute unmodeled news or intraday seasonality to self-excitation; other Hawkes specifications can represent those inputs.
The unmodeled-seasonality limitation applies to a stationary constant-baseline Hawkes specification.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | Bacry, Mastromatteo & Muzy (2015) survey a decade of high-frequency finance built on Hawkes processes: the problems the model has been used for, how it is estimated, and where its assumptions break. |
| Key result / formula | The multivariate form is the workhorse: λ_i(t) = μ_i + Σ_j ∫ φ_ij(t − s) dN_j(s), where the kernel matrix φ encodes who excites whom and the matrix of integrals ∫φ_ij must have spectral radius below one for stationarity. |
| Why it matters for backtesting | A fitted multivariate Hawkes model can provide a conditional benchmark for high-frequency lead-lag claims, provided its event definitions, kernels and observation window are specified. |
What it is
This note is the map of that review; the definition, the branching ratio and its use as a clustering null are in the companion note on self-excitation.
Key result / formula
Three families of application follow. Mid-price dynamics: a two-component process for upward and downward moves whose cross-excitation produces mean reversion at the tick scale while the price stays diffusive at longer horizons — the signature plot and the Epps effect (cross-correlations that vanish as the sampling interval shrinks) come out as consequences of the kernel shape, not separate anomalies. Order-book dynamics: multi-dimensional models of limit, market and cancel orders, and lead-lag between assets. Estimation: parametric maximum likelihood with exponential or power-law kernels, EM on the branching representation, and a non-parametric Wiener-Hopf method that recovers the kernels from second-order statistics without assuming their shape — the option to reach for when the kernel is the object of interest, since a parametric fit imposes the answer.
Why it matters for backtesting
Raw cross-correlation alone need not separate self-excitation from cross-excitation. The chosen kernel affects fitted branching ratios and the interpretation of endogenous activity, so compare plausible specifications and check residual diagnostics. The constant-baseline stationary form displayed above cannot represent time-varying background intensity without an extension; intraday seasonality, news and regime shifts may otherwise be mistaken for self-excitation. Hawkes families can include time-varying or exogenous baselines, so that limitation belongs to the stated specification rather than to all Hawkes models. A causal trading edge does not follow from a fitted excitation parameter alone.
Source
Bacry, Mastromatteo & Muzy, "Hawkes Processes in Finance", Market Microstructure and Liquidity 1(1), 2015, 1550005 (arXiv:1502.04592). Primary source