Half Life OU

Family: Stat-arb

What it computes

Emits HalfLifeOuTick ticks carrying phi_hat, intercept, long_run_mean, half_life_bars, half_life_ms off stock trade tape (5m bars).

Available on the live, historical, and replay drives.

Methodology

Ornstein-Uhlenbeck mean-reversion half-life t₁/₂ = -ln(2) / ln(φ̂) via Yule-Walker (1927) AR(1) on rolling per-bar log prices — Vidyamurthy (2004) pair-trading time-to-mean-reversion clock.

See the methodology overview for the citation index.

Inputs

Stock trade tape (5m bars).

Key outputs

Phi_hat, intercept, long_run_mean, half_life_bars, half_life_ms. The full field set is in the tick table below.

Output schema (HalfLifeOuTick)

The field / type / description table below is regenerated from the HalfLifeOuTick 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).
date	i32	Trading-session date (YYYYMMDD) at emission time.
ms_of_day	i32	Milliseconds since midnight ET at emission time.
phi_hat	f64	AR(1) slope φ̂ = cov(s_t, s_{t-1}) / var(s_{t-1}) over the rolling-window log-price series. φ̂ ∈ (0, 1) flags the stationary mean-reverting regime; φ̂ ≥ 1 flags the non-stationary regime where the OU null is rejected.
intercept	f64	AR(1) intercept â = mean(s_t) − φ̂ · mean(s_{t-1}).
long_run_mean	f64	Long-run equilibrium μ̂ = â / (1 − φ̂) — the log-price level the OU process drifts toward over time.
half_life_bars	f64	OU half-life in bars t₁/₂ = -ln(2) / ln(φ̂). NaN when the AR(1) fit lands outside the stationary mean-reverting region (0, 1).
half_life_ms	f64	OU half-life in milliseconds — half_life_bars * effective_bar_interval_ms. NaN when half_life_bars is NaN.
n_intraday_bars	i32	Count of intraday bars currently inside the rolling window.

Configuration (HalfLifeOuParams)

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

Field	Type	Description
contracts	SecurityFilter	Contracts the subscription tracks. Stocks only.
conditions	ConditionPolicy	Trade-condition admission policy applied to every print.
venues	ExchangeFilter	Exchange / venue admission policy.
bar_interval_ms	i32	Per-bar cadence in milliseconds. Defaults to [DEFAULT_BAR_INTERVAL_MS] (300_000 ms / 5 min).
window_bars	i32	Rolling-window length in bars. Defaults to [DEFAULT_WINDOW_BARS] (78 — one US-equity session).
min_emit_interval_ms	i32	Minimum interval between consecutive emissions per symbol, in milliseconds. Defaults to [DEFAULT_MIN_EMIT_INTERVAL_MS] (60_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().half_life_ou(["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()
  .halfLifeOu(["QQQ"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

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

use kairos::{Client, HalfLifeOuRow};

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

let sub = client
    .live()
    .half_life_ou(["QQQ"])
    .on_event(|row: &HalfLifeOuRow| println!("half_life_bars={} long_run_mean={}", row.half_life_bars, row.long_run_mean))?;
// ... later ...
sub.unsubscribe();
# Ok(())
# }