LeadLagCrossCorrelation

Which of two assets leads the other, and by how many bars. Reports the integer offset k ∈ [−max_lag, max_lag] that maximises |corr(a[t], b[t+k])|, together with the correlation at that lag.

Quick reference

Item	Value
Family	Price Statistics
Input type	(f64, f64) — (a, b) pair
Output type	{ lag: i64, correlation: f64 }
Output range	lag ∈ [−max_lag, max_lag], correlation ∈ [−1, +1]
Default parameters	window = 20, max_lag = 10
Warmup period	window + 2·max_lag
Interpretation	Lead/lag relationship between two assets

Formula

lag = argmax_k | corr( a[t], b[t+k] ) |,   k ∈ [−max_lag, max_lag]

a's window is held fixed in the centre of a window + 2·max_lag buffer while b's window slides across it, so every lag is evaluated only against data already seen (fully causal). Candidate lags are scanned by increasing |k|, so ties resolve to the smallest offset (0 wins an exact tie). Each update is O(window · max_lag). See crates/wickra-core/src/indicators/lead_lag_cross_correlation.rs.

Parameters

Name	Type	Default	Constraint	Description
window	usize	20	>= 2	Points per correlation.
max_lag	usize	10	>= 1	Largest offset searched either way.

Inputs / Outputs

Indicator<Input = (f64, f64), Output = LeadLagCrossCorrelationOutput>. Python update(a, b) returns (lag, correlation) or None; batch(a, b) returns an (n, 2) array with columns [lag, correlation] (NaN warmup). Node returns { lag, correlation }; WASM returns the same object.

Warmup

warmup_period() == window + 2·max_lag.

Edge cases

• Flat channel. A constant a or b has zero variance ⇒ every correlation is 0 and the reported lag is 0.
• Positive vs negative lag. Positive ⇒ a leads b; negative ⇒ b leads a; 0 ⇒ most correlated contemporaneously.
• Reset. Clears both ring buffers.

Examples

Rust

use wickra::{Indicator, LeadLagCrossCorrelation};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut ll = LeadLagCrossCorrelation::new(12, 5)?;
    for t in 0..60 {
        let a = (f64::from(t) * 0.4).sin();
        let b = (f64::from(t - 3) * 0.4).sin(); // b lags a by 3
        if let Some(o) = ll.update((a, b)) {
            // o.lag converges to +3 (a leads b by 3)
            let _ = o;
        }
    }
    Ok(())
}

Python

import numpy as np
import wickra as ta

t = np.arange(60)
a = np.sin(t * 0.4)
b = np.sin((t - 3) * 0.4)            # b lags a by 3
out = ta.LeadLagCrossCorrelation(12, 5).batch(a, b)
print(int(out[-1, 0]))               # 3  (a leads b)

Node

const wickra = require('wickra');
const ll = new wickra.LeadLagCrossCorrelation(12, 5);
const { lag, correlation } = ll.update(a, b) ?? {};

Interpretation

• lag > 0. a leads b — a's moves show up in b lag bars later; trade b off a's signal.
• lag < 0. b leads a.
• correlation sign. Positive ⇒ same-direction lead; negative ⇒ inverse.

Common pitfalls

• Periodic signals. A pure sinusoid correlates with many shifts; the detected lag can be ambiguous. Use returns or de-trended series.
• Look-ahead. This indicator is causal by construction — it never uses future b to assess a negative lag.

See also

• PearsonCorrelation — contemporaneous correlation (the lag = 0 special case).
• Autocorrelation — single-series lagged correlation.
• Indicators-Overview — full taxonomy.