The Quadrant Probabilities of Paired Financial Time Series

This paper introduces the quadrant probability as a new instrument to evaluate the correlation and co-movement between a pair of financial time series. We pair several stocks and indices and examine the pattern of the corresponding quadrant probabilities. To better understand the behavior of the quadrant probabilities, we start from using the centric bivariate normal probability to simulate two correlated time series, and then we generalize it into the non-centric case. In the non-centric case, we construct a method to estimate the quadrant probability series with rolling linear regressions and numerical integration. We find that our approach not only reproduces the pattern of the observed quadrant probability series but also holds sensitivity with respect to the correlation between the two time series. In other words, our approach successfully captures the correlation and the co-movement pattern of the pair of time series