Cointegration Half-Life Solver

How long it takes for half of a cointegrated spread's deviation from equilibrium to mean-revert. From the Ornstein-Uhlenbeck speed-of-mean-reversion parameter θ: half-life = ln(2) / θ. Pairs with half-life under 30 days are typically tradeable; above 90 days, the alpha decays before round-trip costs are recovered.

Linear regression of Δspread_t on spread_(t-1). The regression slope is -θ. The methodology page documents the OLS form and the standard error, plus a check on residual autocorrelation (Ljung-Box) — if residuals aren't white, the OU model is mis-specified and the half-life estimate is unreliable.

Yes — Engle-Granger two-step test (ADF on the residuals from the cointegrating regression) and Johansen test for the rank of the cointegrating relationship. The tool refuses to compute half-life if the test rejects cointegration; the methodology explains why a half-life on a non-cointegrated series is meaningless.

Highly. Estimating from 6 months gives a different number than 5 years. The tool computes half-life across rolling 1-year, 3-year, and full-sample windows and flags pairs where the estimate is unstable across windows. Stability matters more than the absolute number.

The math doesn't care about asset class — it works for stock pairs, ETF arbitrage, crypto pairs, FX pairs. But the cointegration premise (a stable long-run equilibrium) is most credible for assets with structural linkage: dual-listed shares, ETF-vs-creation-basket, futures-vs-cash. Speculative pair trades on non-linked assets often produce false-positive cointegration tests.