Hurst Exponent

Family: Stat-arb

What it computes

Emits HurstExponentTick ticks carrying hurst, rescaled_range, range, stddev, n_intraday_bars off stock trade tape (5m bars).

Available on the live, historical, and replay drives.

Methodology

Mandelbrot-Wallis (1969) rescaled-range R/S with the Anis-Lloyd (1976) centered estimator H = ½ + (ln(R/S) − ln E₀[R/S_N])/ln(N) and the Weron (2002) finite-sample factor, over rolling per-bar log returns.

See the methodology overview for the citation index.

Inputs

Stock trade tape (5m bars).

Key outputs

Hurst, rescaled_range, range, stddev, n_intraday_bars. The full field set is in the tick table below.

Output schema (HurstExponentTick)

The field / type / description table below is regenerated from the HurstExponentTick 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.
hurst	f64	Anis-Lloyd-centred rescaled-range Hurst exponent H = ½ + (ln(R/S) − ln E₀[R/S_N]) / ln(N). H > 0.5 flags the trending regime; H < 0.5 flags the mean-reverting regime; H ≈ 0.5 flags the geometric Brownian null.
rescaled_range	f64	Rescaled range R / S — the unstandardised statistic the scaling law is fit against.
range	f64	Range R = max(y_t) − min(y_t) of the cumulative deviation from the sample mean.
stddev	f64	Sample standard deviation S = sqrt((1 / N) · Σ (r_i − μ)²) of the per-bar log returns over the window.
n_intraday_bars	i32	Count of intraday bars currently inside the rolling window.

Configuration (HurstExponentParams)

Regenerated from the HurstExponentParams 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().hurst_exponent(["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()
  .hurstExponent(["QQQ"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

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

use kairos::{Client, HurstExponentRow};

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

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