Demonstrating error-correction modelling for intraday statistical arbitrage

Abstract

Applying cointegration analysis to security price movements illustrates how securities move together in the long-term. This can be augmented with an error-correction model to show how the long-run relationship is approached when the security prices are out of line with their cointegrated relationship. Cointegration and error-correction modelling promises to be useful in statistical arbitrage applications: not only does it show what relative prices of securities should be, but it also illuminates the short-run dynamics of how equilibrium should be restored along with how long it will take. Cointegration, coupled with error-correction modelling, promises to be a profitable way of implementing statistical arbitrage strategies. 1 Bondarenko (2003) and Hogan et al. (2004) defined statistical arbitrage as an attempt to exploit the long-horizon trading opportunities revealed by cointegration relationships. Alexander and Dimitriu (2005) showed how cointegration is a better way of implementing a statistical arbitrage strategy than other conventional ways, like the use of tracking error variance minimization. These previous studies, however, did not add error-correction modelling to the trading strategies. This article seeks to fill that gap, by presenting how to implement a statistical arbitrage strategy based on cointegration and error-correction modelling. 1 For example, see Kumar and Seppi (1994), Wang and Yau (1994), Forbes et al. (1999), Canjels et al. (2004), Tatom (2002), Harasty and Roulet (2000) and Laopodis and Sawhney (2002). They have applications ranging from index arbitrage to gold-point arbitrage during the pre-World War I era.