Learning and Trusting Cointegration in Statistical Arbitrage

Abstract

The paper offers adaptation of cointegration analysis for statistical arbitrage. Cointegration is a structural relationship model that relies on dynamic correction towards the equilibrium. The model is ultimately linear: when relationships are decoupled, the forecast of individual price follows a linear trend over the long term. 'Error correction' terminology does not apply to forecasting and therefore, is misleading.

Dynamic correction towards the equilibrium realises as a mean-reverting feature of the spread generated by the cointegrated relationship. Quality of mean-reversion defines suitability for statistical arbitrage and is evaluated by fitting to the Ornstein-Uhlenbeck process. Trade design cannot rely on standard cointegration tests due to their low power; their formulation is incompatible with the GBM process for asset price. However, the econometric specification of equilibrium correction is compatible with the OU process fit.

There are two technical appendices. Appendix A collects time series decompositions and derivations frequently omitted in presentation of the equilibrium correction. Appendix B discusses the common issues of equity pairs trading that relies on simple cointegration.

Keywords: time series decomposition, forecasting, cointegration, equilibrium correction, mean-reversion, Ornstein-Uhlenbeck, spread trading, statistical arbitrage

JEL Classification: C5, C62, G10