Detecting Mean-Reverted Patterns in Algorithmic Pairs Trading

Abstract

This paper proposes a methodology for detecting mean-reverted segments of data streams in algorithmic pairs trading. Considering a state-space model that describes the spread (data stream) as the difference of the prices of two assets, we propose two new recursive least squares (RLS) algorithms for predicting mean-reversion of the spread in real time. The first is a combination of steepest descent RLS and Gauss–Newton RLS, for which we extend previous work by providing exact recursive equations to update the variable forgetting factor (VFF). We propose a new RLS algorithm for variable forgetting, by transforming the prediction errors into a binary process and adopting Bayesian methods for inference. The new approach is versatile as compared to more traditional RLS schemes, having the advantage of uncertainty analysis around the VFF. The methods are illustrated with real data, consisting of daily prices of Target Corporation and Walmart Stores Inc shares, over a period of 6 years. Alongside the detection of mean-reversion of the spread, we implement a simple trading strategy. The empirical results suggest that the new Bayesian approach returns are in excess of 130% cumulative profit over a period of 2 years.