wickra/docs/wiki/indicators/volatility/Indicator-StdDev.md

StdDev

Rolling population standard deviation — the dispersion of the last period prices around their mean.

Quick reference

Field	Value
Family	Volatility
Sub-category	Dispersion
Input type	f64 (single close)
Output type	f64
Output range	[0, ∞) (price-difference scale)
Default parameters	period = 20 (Python)
Warmup period	period
Interpretation	Spread of recent prices; the raw volatility behind Bollinger Bands.

Formula

mean     = (1/n) · Σ price
variance = (1/n) · Σ price² − mean²
StdDev   = √variance

This is the population standard deviation (divisor n, not n − 1) — the exact dispersion measure that drives the band width of BollingerBands. It is maintained as an O(1) state machine: a running sum and a running sum-of-squares, each updated by one add and one subtract per bar. Floating-point cancellation can leave the computed variance very slightly negative; it is clamped to zero before the square root.

Parameters

Name	Type	Default	Valid range	Description
period	usize	20 (Python)	>= 1	Rolling window length. 0 errors with Error::PeriodZero. period = 1 always yields 0.

The Python binding defaults period to 20.

Inputs / Outputs

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

impl Indicator for StdDev {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

StdDev::new(period).warmup_period() == period. The first non-None value is emitted once the window holds period prices.

Edge cases

• Constant series. A flat series has zero dispersion, so the output is 0.0 (constant_series_yields_zero pins this).
• NaN / infinity inputs. Non-finite inputs are silently dropped; the window and the running sums are left untouched.
• Reset. sd.reset() clears the window and both running sums.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut sd = StdDev::new(3)?;
    let out: Vec<Option<f64>> = sd.batch(&[2.0, 4.0, 6.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(1.6329931618554525)]

The window [2, 4, 6] has mean 4 and variance (4 + 0 + 4) / 3 = 8/3, so the standard deviation is √(8/3) ≈ 1.633. This matches the reference_value test in crates/wickra-core/src/indicators/std_dev.rs.

Python

import numpy as np
import wickra as ta

sd = ta.StdDev(3)
print(sd.batch(np.array([2.0, 4.0, 6.0])))

Output:

[      nan       nan 1.6329932]

Node

const ta = require('wickra');
const sd = new ta.StdDev(3);
console.log(sd.batch([2, 4, 6]));

Output:

[ NaN, NaN, 1.6329931618554525 ]

Interpretation

StdDev is the most direct volatility measure in the library: large values mean prices are scattered widely around their mean, small values mean a tight, quiet market. Use it on its own as a volatility filter, or recognise it as the engine inside BollingerBands — multiplying StdDev by the band multiplier and adding it to an Sma reproduces the bands exactly.

Common pitfalls

• Expecting the sample standard deviation. StdDev divides by n, not n − 1. For the unbiased return-based estimator use HistoricalVolatility.
• Comparing across instruments. The output is in price units; a StdDev of 5 is not comparable between a $10 and a $1000 asset.

References

The population standard deviation is standard statistics; this implementation matches the dispersion term of John Bollinger's Bollinger Bands and pandas' rolling(period).std(ddof=0).

See also

• Indicator-BollingerBands.md — bands built from this dispersion measure.
• Indicator-HistoricalVolatility.md — annualised volatility of log returns.
• Indicators-Overview.md — the full taxonomy.