Skewness

Rolling Pearson skewness (third standardised central moment) of the last period values. Positive skewness means the right tail is heavier than the left; negative skewness flags the opposite. A symmetric distribution has skewness 0.

Quick reference

Item	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	unbounded
Default parameters	period required
Warmup period	period
Interpretation	Distribution asymmetry; financial returns typically -0.5 to -2

Formula

mean = (1/n) · Σ x
m2   = (1/n) · Σ (x - mean)²        (population variance)
m3   = (1/n) · Σ (x - mean)³        (third central moment)
Skew = m3 / m2^(3/2)

Population formula with divisor n. See crates/wickra-core/src/indicators/skewness.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	>= 3	Rolling window.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Standard binding shapes.

Warmup

warmup_period() == period.

Edge cases

• m2 = 0. Constant input; skew undefined → returns 0.0.
• Sample size. Skew is noisy on small windows; ≥ 50 bars recommended.
• Reset. Clears the rolling window.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut series: Vec<f64> = (0..100).map(|i| f64::from(i) * 0.1).collect();
    series[50] = 50.0;  // positive outlier
    let mut s = Skewness::new(50)?;
    println!("row 80 = {:?}", s.batch(&series)[80]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

series = np.arange(100, dtype=float) * 0.1
series[50] = 50.0
s = ta.Skewness(50)
print(s.batch(series)[80])  # positive skew

Node

const wickra = require('wickra');
const s = new wickra.Skewness(50);
const series = Array.from({ length: 100 }, (_, i) => i * 0.1);
series[50] = 50.0;
console.log(s.batch(series)[80]);

Streaming

use wickra::{Indicator, Skewness};

let mut s = Skewness::new(252).unwrap();
let return_stream: Vec<f64> = Vec::new(); // your stream of periodic returns
for daily_return in return_stream {
    if let Some(v) = s.update(daily_return) {
        if v < -1.0 { /* heavy left tail — drawdown risk elevated */ }
    }
}

Interpretation

• Positive skew. Right tail heavier — occasional large positive moves. Trend-following / momentum strategies tend to produce positively skewed returns.
• Negative skew. Left tail heavier — occasional large negative moves. Typical for equity index returns; mean-reversion strategies often produce negative skew.
• Skew = 0. Symmetric — likely Gaussian or symmetric bimodal.
• Pair with Kurtosis. Skewness tells you which tail is heavier; kurtosis tells you how heavy the tails are overall.

Common pitfalls

• Sample-size noise. Same caveat as Kurtosis — small windows give noisy estimates. Use ≥ 50 bars.
• Population vs sample. Wickra uses population (n divisor). pandas uses sample with bias correction (Fisher-Pearson). The two differ by ~5% for n = 50.
• Outlier sensitivity. Single large outlier dramatically inflates skew. Intentional — that's what it measures.

References

• Standard statistics; documented in any introductory text.
• For finance applications: Mandelbrot, The Variation of Certain Speculative Prices, Journal of Business, 1963 — first formal recognition of non-Gaussian return distributions in finance.

See also

• Kurtosis — fourth-moment sibling.
• Variance — second-moment.
• StdDev — sqrt of Variance.
• Indicators-Overview — full taxonomy.