JarqueBera

The Jarque-Bera statistic on a rolling window — a normality test that flags fat-tailed or skewed return regimes from skewness and excess kurtosis.

Quick reference

Field	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	[0, ∞) (0 = perfectly normal sample)
Default parameters	(period = 50) (Python)
Warmup period	period
Interpretation	> ~6 rejects normality at 95% (χ², 2 d.o.f.).

Formula

S  = skewness        = m3 / m2^(3/2)
K  = excess kurtosis = m4 / m2² − 3
JB = (period / 6) · ( S² + K²/4 )

m2, m3, m4 are the central moments of the window. A normal sample has zero skew and zero excess kurtosis → JB = 0. The statistic grows with asymmetry and with fat (or thin) tails, and under the normality null is asymptotically χ² with two degrees of freedom — so values above ~6 reject normality at the 95% level. Source: crates/wickra-core/src/indicators/jarque_bera.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	50 (Python)	>= 4	jarque_bera.rs:54	Rolling window length. 0 errors with Error::PeriodZero; < 4 errors with Error::InvalidPeriod.

The period getter returns the window; value returns the current output if ready.

Inputs / Outputs

From crates/wickra-core/src/indicators/jarque_bera.rs:

use wickra::{Indicator, JarqueBera};
// JarqueBera: Input = f64, Output = f64
const _: fn(&mut JarqueBera, f64) -> Option<f64> = <JarqueBera as Indicator>::update;

An f64 in, an Option<f64> out. The Python binding takes a scalar for update and a 1-D numpy array for batch (NaN warmup); Node takes update(value) and batch(values[]). Feed it a return series for the usual normality check.

Warmup

warmup_period() == period. The first value lands once the window is full (first_emission_at_warmup_period pins this).

Edge cases

• Constant window → 0. Zero variance (m2 == 0) returns 0 (constant_window_is_zero pins this).
• Non-negative. JB ≥ 0 by construction (output_is_non_negative pins this).
• Skew/kurtosis ordering. A window with a heavy outlier scores far above a symmetric one (skewed_window_exceeds_symmetric pins this).
• Non-finite input. A NaN/∞ input is ignored and the last value returned (ignores_non_finite pins this).
• Reset. jb.reset() clears the window and the last value (reset_clears_state).

Examples

Rust

use wickra::{BatchExt, Indicator, JarqueBera};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut jb = JarqueBera::new(8)?;
    // A symmetric window scores low.
    let out = jb.batch(&[-3.0, -1.0, 0.0, 1.0, 3.0, -2.0, 2.0, 0.0]);
    println!("{:?}", out.last().unwrap());
    Ok(())
}

Output (small, near zero — close to normal):

Some(0.41...)

Python

import numpy as np
import wickra as ta

jb = ta.JarqueBera(50)
returns = np.diff(np.log(100 + np.cumsum(np.random.randn(200))))
print(jb.batch(returns)[-1])   # high in fat-tailed regimes

Node

const ta = require('wickra');

const jb = new ta.JarqueBera(50);
console.log('warmupPeriod:', jb.warmupPeriod()); // 50

Streaming

use wickra::{Indicator, JarqueBera};

let mut jb = JarqueBera::new(50).unwrap();
let mut last = None;
for i in 0..80 {
    last = jb.update((f64::from(i) * 0.3).sin());
}
println!("{last:?}");

Streaming update and batch are equivalent tick-for-tick (batch_equals_streaming pins this).

Interpretation

1. Tail-risk flag. A rising JB on a return window warns that the distribution is fattening — drawdown and gap risk are elevated.
2. Model sanity. Strategies that assume Gaussian returns (mean-variance sizing, many option models) misbehave when JB rejects normality.
3. Regime split. Threshold JB at the χ² critical value to bucket the market into "normal" vs. "non-normal" periods for conditional back-tests.

Common pitfalls

• Feed returns, not prices. Normality is a property of returns; on raw trending prices JB is large but meaningless.
• Small-sample bias. Below ~30 observations the χ² approximation is rough; treat short-window readings qualitatively.
• Two failure modes. A high JB can come from skew or kurtosis; inspect Skewness and Kurtosis to tell which.

References

Jarque, C. M., & Bera, A. K. (1980), "Efficient tests for normality, homoscedasticity and serial independence of regression residuals", Economics Letters.

See also

• Indicator-Skewness — third-moment asymmetry.
• Indicator-Kurtosis — fourth-moment tailedness.
• Indicator-ShannonEntropy — distributional entropy.
• Indicators-Overview — the full taxonomy.