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Learning and Trusting Cointegration in Statistical Arbitrage

27 Pages Posted: 22 Feb 2013 Last revised: 30 Sep 2014

Richard V. Diamond

Fitch Group; CQF Institute

Date Written: September 30, 2014


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

Suggested Citation

Diamond, Richard V., Learning and Trusting Cointegration in Statistical Arbitrage (September 30, 2014). Available at SSRN: or

Richard V. Diamond (Contact Author)

Fitch Group ( email )

30 North Colonnade
Canary Wharf
London, E14 5GN
United Kingdom

CQF Institute ( email )

55 Broad Street
New York, NY 10004
United States

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