High Frequency Statistical Arbitrage Via the Optimal Thermal Causal Path

We consider the problem of identifying similarities and causality relationships in a given set of financial time series data streams. We develop further the Optimal Thermal Causal Path method proposed by Sornette et al, which is a non-parametric method proposed by Sornette et al. The method considers the mismatch between a given pair of time series in order to identify the expected minimum energy path lead-lag structure between the pair. Traders may find this a useful tool for directional trading, to spot arbitrage opportunities. We add a curvature energy term to the method and we propose an approximation technique to reduce the computational time. We apply the method and approximation technique on various market sectors of NYSE data and extract the highly correlated pairs of time series. We show how traders could exploit arbitrage opportunities by using the method.