Spearman Rank Correlation

Rolling Spearman rank correlation between two synchronised series. Captures monotonic rather than linear association — values in each channel are replaced by their ranks (mid-ranks for ties), and the Pearson correlation of those ranks is reported. Robust to nonlinearities that defeat Pearson.

Quick reference

Item	Value
Family	Price Statistics
Input type	(f64, f64) — (x, y) pair per update
Output type	f64
Output range	[-1, +1]
Default parameters	period required
Warmup period	period
Interpretation	Strength of monotonic relationship (linear or nonlinear)

Formula

rx = rank(x_i)  with mid-rank tie handling
ry = rank(y_i)  with mid-rank tie handling
Spearman = Pearson(rx, ry)

Mid-rank tie handling assigns the average rank to tied values (matches scipy's default). See crates/wickra-core/src/indicators/spearman_correlation.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Rolling window.

Inputs / Outputs

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

Warmup

warmup_period() == period.

Edge cases

• All-tied input. Variance of ranks zero → output 0.0.
• Monotone but nonlinear relationship. Pearson may show low correlation; Spearman shows ±1.
• Cost. Each update is O(period · log period) due to sort.
• Reset. Clears the rolling window.

Examples

Rust

use wickra::{Indicator, SpearmanCorrelation};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut s = SpearmanCorrelation::new(50)?;
    for i in 0..100 {
        let x = f64::from(i);
        let y = x.powi(2);  // monotone nonlinear
        let _ = s.update((x, y));
    }
    Ok(())
}

Python

import numpy as np
import wickra as ta

x = np.arange(100, dtype=float)
y = x ** 2
s = ta.SpearmanCorrelation(50)
print(s.batch(x, y)[-1])  # +1.0 (perfectly monotone)

Node

const wickra = require('wickra');
const s = new wickra.SpearmanCorrelation(50);
// feed x, y

Streaming

use wickra::{Indicator, SpearmanCorrelation};

let mut s = SpearmanCorrelation::new(252).unwrap();
let price_stream: Vec<(f64, f64)> = Vec::new(); // your paired (a, b) feed
for (asset_a, asset_b) in price_stream {
    if let Some(v) = s.update((asset_a, asset_b)) {
        // v is rolling rank correlation — robust to nonlinearity
    }
}

Interpretation

• Spearman ≈ +1. Perfect monotone increasing relationship (linear OR nonlinear).
• Spearman ≈ -1. Perfect monotone decreasing.
• Vs Pearson. Pearson detects only linear; Spearman detects any monotone relationship. For two series related by y = x² (positive x): Pearson ≈ 0.97; Spearman = 1.0.
• Outlier robustness. Ranks bound outliers — Spearman is more robust than Pearson to extreme values.

Common pitfalls

• Slower than Pearson. O(n log n) per update vs O(1).
• Tie handling. Series with many tied values produce ambiguous ranks; mid-rank handling is standard but other conventions exist.
• Confusing with Kendall's tau. Kendall's tau is another rank correlation; computationally more expensive, slightly different formula. Wickra implements Spearman.

References

• Charles Spearman, The Proof and Measurement of Association between Two Things, American Journal of Psychology, 1904.

See also

• PearsonCorrelation — linear cousin.
• Beta — regression slope (related but different).
• Indicators-Overview — full taxonomy.