Hawkes Intensity

Family: Microstructure

What it computes

Emits HawkesIntensityTick ticks carrying lambda_now, α, branching_ratio, is_stable off trade arrival times.

Available on the live, historical, and replay drives.

Methodology

Hawkes (1971) self-exciting intensity via the rate-invariant inter-arrival CV² branching proxy; Bacry-Mastromatteo-Muzy (2015) Fano regression is the designated upgrade.

See the methodology overview for the citation index.

Inputs

Trade arrival times.

Key outputs

Lambda_now, α, branching_ratio, is_stable. The full field set is in the tick table below.

Output schema (HawkesIntensityTick)

The field / type / description table below is regenerated from the HawkesIntensityTick Rust source by docs-site/scripts/inject-doc-tables.ts on every npm run docs:build. Do not hand-edit between the sentinels.

Field	Type	Description
symbol	Arc<str>	Underlying symbol (interned). Stock-only analytic — the symbol is the full user-facing identity.
date	i32	Trading-session date (YYYYMMDD).
ms_of_day	i32	Milliseconds since midnight at emission time.
lambda_current	f64	Conditional intensity at emit time, in arrivals per second λ(t_emit) = μ + α · Σ exp(−β · (t_emit − tᵢ)). NaN under the documented degenerate-window guard.
mu_baseline	f64	Baseline arrival-rate estimate μ̂ = n / window_seconds in arrivals per second.
alpha_excitation	f64	Excitation parameter α̂ recovered from the rolling-window inter-arrival CV² surplus, scaled by the decay β. NaN with fewer than three samples.
branching_ratio	f64	Branching ratio α̂ / β — stationarity diagnostic per Bacry-Mastromatteo-Muzy (2015). Values approaching one indicate near-explosive self-excitation; values at or above one render the process non-stationary.
trades_in_window	i32	Number of admitted trade arrivals currently inside the window.
is_stable	bool	true when the recovered α̂ / β < 1 — the Bacry-Mastromatteo-Muzy stationarity bound. false flags a non-stationary regime under which lambda_current should be consumed with a Poisson-fallback caveat.

Configuration (HawkesIntensityParams)

Regenerated from the HawkesIntensityParams Rust source — see the note above.

Field	Type	Description
contracts	SecurityFilter	Contracts the subscription tracks. The Hawkes estimator runs off the stock trade tape — the filter must resolve to stock contracts.
conditions	ConditionPolicy	Trade-condition admission policy applied to every print.
venues	ExchangeFilter	Exchange / venue admission policy.
window_ms	i32	Rolling-window length in milliseconds. Defaults to [DEFAULT_WINDOW_MS] (60_000 ms).
decay_per_second	f64	Hawkes decay parameter β in per-second units. Defaults to [DEFAULT_DECAY_PER_SECOND] (1.0). Fixed rather than fit per emit per the methodology note above.
min_emit_interval_ms	i32	Minimum interval between consecutive emissions per symbol, in milliseconds. Defaults to [DEFAULT_MIN_EMIT_INTERVAL_MS] (1_000 ms).

Example

Python

import kairos_thetadata as kt

client = kt.Client.connect(kt.Credentials.from_env())

def on_event(row):
    print(row)

sub = client.live().hawkes_intensity(["QQQ"]).on_event(on_event)
sub.wait(timeout_seconds=60.0)

TypeScript

import { Client, Credentials } from "kairos-thetadata";

const client = await Client.connect(Credentials.fromEnv());

await client
  .live()
  .hawkesIntensity(["QQQ"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

// Cargo.toml:
//   kairos = "0.1"

use kairos::{Client, HawkesIntensityRow};

# fn run() -> Result<(), Box<dyn std::error::Error>> {
let client = Client::connect(("me@example.com", "secret"))?;

let sub = client
    .live()
    .hawkes_intensity(["QQQ"])
    .on_event(|row: &HawkesIntensityRow| println!("lambda_current={} branching_ratio={}", row.lambda_current, row.branching_ratio))?;
// ... later ...
sub.unsubscribe();
# Ok(())
# }