Lead-Lag

How the platform identifies which asset moves first and which follows, using cross-correlation analysis across time shifts.

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Concept

Standard correlation asks: "Do A and B move together?"

Lead-lag asks: "Does A at time T predict B at time T+k?"

The answer is found by computing Pearson correlation between the two return series at every possible time shift (lag).

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Input: Percent Returns

Like all analytics on the platform, lead-lag operates on percent returns:

r(t) = (price(t) - price(t-1)) / price(t-1) × 100

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Cross-Correlation at a Single Lag

For lag k, one series is shifted relative to the other and Pearson correlation is computed:

function crossCorrAtLag(ra, rb, k) {
  if (k === 0) return pearson(ra, rb);
  if (k > 0)   return pearson(ra.slice(0, ra.length-k), rb.slice(k));
  return               pearson(ra.slice(-k), rb.slice(0, rb.length+k));
}

Lag k	What it measures
k = 0	Simultaneous correlation (same as Pearson)
k > 0	Does A at time t predict B at time t+k? → A leads
k < 0	Does B at time t predict A at time t+k? → B leads

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Full Cross-Correlation Function

The platform sweeps lags from -maxLag to +maxLag and collects correlation at each step:

function crossCorrFull(ra, rb, maxLag) {
  const out = [];
  for (let k = -maxLag; k <= maxLag; k++) {
    const v = crossCorrAtLag(ra, rb, k);
    if (v !== null) out.push({ lag: k, corr: v });
  }
  return out;
}

The result is the Cross-Correlation Function (CCF) chart.

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Finding the Lead-Lag Relationship

The dominant lead-lag is the lag k where |correlation| is maximum:

function findLeadLag(symA, symB, ra, rb, maxLag) {
  const pts = crossCorrFull(ra, rb, maxLag);
  const best = pts.reduce((a,b) => Math.abs(b.corr) > Math.abs(a.corr) ? b : a);
  return {
    leader:    best.lag >= 0 ? symA : symB,
    follower:  best.lag >= 0 ? symB : symA,
    lagBars:   Math.abs(best.lag),
    corrAtLag: best.corr,
    corrAt0:   pts.find(p => p.lag === 0)?.corr ?? null,
    pts,
  };
}

Reading the Result

best.lag	Interpretation
+5	A leads B by 5 ticks
-3	B leads A by 3 ticks
0	Simultaneous — neither leads

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Lag Windows

Window	Tick range	1 tick ≈
1m	±20 ticks	~3 seconds
5m	±20 ticks	~15 seconds
15m	±20 ticks	~45 seconds
1h	±20 ticks	~3 minutes

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Reading the CCF Chart

The chart plots correlation at every lag from -20 to +20:

• Peak position → direction and magnitude of lead-lag

• Peak height → strength of the predictive relationship

• Flat curve → no lead-lag, assets react independently

• Multiple peaks → noisy or unstable relationship

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corrAt0 vs corrAtLag

Metric	Description
corrAt0	Standard Pearson at zero lag — same as Matrix
corrAtLag	Correlation at the optimal lag — the predictive signal

If corrAtLag >> corrAt0, the relationship is primarily predictive (one leads the other) rather than simultaneous.

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Oracle Timing Note

Pyth Hermes pushes updates per asset independently. A lag of 1–2 ticks may reflect oracle update timing rather than true price discovery. Lags of 3+ ticks are more likely to reflect genuine market microstructure.