Lead–lag structure between prediction markets and equities

Hypothesis: on well-defined macro events, prediction market prices update before the corresponding equity or crypto reaction — often by minutes — and the lead is measurable.

Setup

For a prediction market price series $p_t$ (a probability) and an asset return series $r_t$, estimate the lagged cross-correlation

$$\rho(\tau) = \operatorname{corr}\big(\Delta p_{t}, \; r_{t+\tau}\big)$$

and look for the $\tau^\* = \arg\max_\tau |\rho(\tau)|$. A positive $\tau^\*$ means the prediction market leads.

Pitfalls found so far

Pitfall	Symptom	Fix
Stale quotes on thin markets	spurious "lead" from interpolation	trade-time sampling, not clock-time
Non-synchronous trading hours	correlations at absurd lags	restrict to overlapping sessions
Event clustering	one FOMC day dominates the estimate	per-event normalization

First honest result

On a small sample of rate-decision events, the point estimate of the lead is positive but the confidence interval still straddles zero. Which is the correct outcome for this amount of data — the interesting work is building the event library large enough for the interval to tighten one way or the other.

def lead_lag(dp, r, max_lag):
    return {
        tau: np.corrcoef(dp[:-tau or None], r[tau:])[0, 1]
        for tau in range(1, max_lag)
    }

Next: switch from Pearson correlation to a Hawkes-style excitation model, so bursts of prediction-market trades can be treated as events rather than increments.