Three takes on the same pair.
The cointegration approach (rolling OLS + z-score), the original empirical distance method (Gatev et al.), and the OU-equilibrium s-score (Avellaneda & Lee) — all running on the same synthetic pair, with the same costs and slippage. Different views of the same truth often disagree on the easy pairs and converge on the hard ones.
Equity curves overlaid
all start at 1.0Cointegration (Engle-Granger + z-score)
Engle-Granger 1987 / Vidyamurthy 2004
Distance method (Gatev-Goetzmann-Rouwenhorst)
Gatev, Goetzmann, Rouwenhorst 2006
OU s-score (Avellaneda-Lee single-factor)
Avellaneda & Lee 2010
When each approach wins
Cointegration is the textbook winner when the cointegration coefficient is stable and the spread reverts at a tractable speed — the rolling z-score adapts naturally as drift changes.
Distance methodrequires no parametric assumptions and is the most robust to estimation noise. Its weakness is that it implicitly assumes β = 1, so it under-performs when α ≠ 1 or when the normalisation drifts (Do & Faff 2010 traced most of its post-2002 decline to this).
OU s-scoreshines when the spread really is well-described by an OU process: it standardises by the equilibrium dispersion rather than rolling moments, so signals are calibrated to the SDE rather than to the most-recent volatility regime. It performs poorly when (μ, σ_OU) shift mid-sample — e.g. on the "Broken" pair.
Disagreement between the three is informative on its own: a pair that all three love is genuinely tradable; a pair that only one likes is suspicious.