Learning and Trusting Cointegration in Statistical Arbitrage

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