RollingQuantile

The interpolated quantile-th quantile of the last period values (type-7 / NumPy-default definition).

Quick reference

Field	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	within [min, max] of the window
Default parameters	period and quantile ∈ [0, 1] are required
Warmup period	period
Interpretation	quantile = 0.5 is the rolling median; 0.0/1.0 are the window min/max.

Formula

h        = (period − 1) · quantile
lower    = ⌊h⌋
result   = sorted[lower] + (h − lower) · (sorted[lower + 1] − sorted[lower])

This is the type-7 / NumPy-default quantile: it interpolates linearly between the bracketing order statistics, so quantile = 0.0 returns the window minimum, 0.5 the median, 1.0 the maximum. Each update copies the window into a scratch buffer and sorts it (NaN-safe total ordering).

Source: crates/wickra-core/src/indicators/rolling_quantile.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 1	rolling_quantile.rs:56	Window length. 0 errors with Error::PeriodZero.
quantile	f64	none	[0.0, 1.0] finite	rolling_quantile.rs:56	Order statistic to select. Out-of-range / NaN errors with Error::InvalidParameter.

(The Python class is wickra.RollingQuantile(period=20, quantile=0.5).)

Inputs / Outputs

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

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

Python streams as float | None, batches as a 1-D numpy.ndarray. Node streams as number | null, batches as Array<number>.

Warmup

warmup_period() == period: the first value is emitted once the window is full. The unit test accessors_and_metadata pins warmup_period() == 14 for period = 14.

Edge cases

• Median. For a full window, quantile = 0.5 returns the median; the unit test median_of_window pins it ([5,1,3,2,4] → 3).
• Min / max. quantile = 0.0/1.0 return the window extremes; pinned by min_and_max_quantiles.
• Interpolation. For sorted = [10,20,30,40], quantile = 0.25 gives 17.5; pinned by interpolated_quantile.
• Single-period window. period = 1 returns the only value verbatim; pinned by single_period_returns_value.
• Reset. reset() clears the window and scratch buffer.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut q = RollingQuantile::new(5, 0.5)?;
    let out: Vec<Option<f64>> = q.batch(&[5.0, 1.0, 3.0, 2.0, 4.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, None, None, Some(3.0)]

The sorted window [1,2,3,4,5] has median 3.

Python

import wickra as ta

q = ta.RollingQuantile(5, 0.5)
for x in [5.0, 1.0, 3.0, 2.0, 4.0]:
    print(x, '->', q.update(x))

Output:

5.0 -> None
1.0 -> None
3.0 -> None
2.0 -> None
4.0 -> 3.0

Node

const ta = require('wickra');
const q = new ta.RollingQuantile(5, 0.5);
for (const x of [5, 1, 3, 2, 4]) console.log(x, '->', q.update(x));

Output:

5 -> null
1 -> null
3 -> null
2 -> null
4 -> 3

Interpretation

Rolling quantiles turn any series into distribution-aware thresholds: a price above its rolling 90th percentile is stretched; volatility split at the 25th/75th percentiles defines regimes (this is the building block of RegimeLabel); robust band edges ignore the tails. The median (quantile = 0.5) is a robust alternative to a moving average.

Common pitfalls

• Cost. Each update sorts the window (O(period log period)). For very large periods on hot paths this is heavier than a running mean — keep the window modest.
• Quantile vs percentile. quantile here is a fraction in [0, 1], not a percentile in [0, 100]. Pass 0.9, not 90.

References

The type-7 linear-interpolation definition is the default in NumPy (numpy.quantile) and Hyndman & Fan (1996), method 7.

See also

• Indicator-RollingIqr — Q3 − Q1 built on the same quantiles.
• Indicator-MedianAbsoluteDeviation — robust dispersion.
• Indicators-Overview — the full taxonomy.