Quantile transfer entropy: Measuring the heterogeneous information transfer of nonlinear time series

Abstract

Due to the existence of the nonlinear mechanism in complex systems, a large event is more likely to arise the impacts substantially different from those of a small event. Although this opinion is widely accepted, detecting their differences have been few reported, especially on the information transfer analysis. In this paper, we consider the heterogeneous information transfer between two nonlinear time series, and propose a new method called quantile transfer entropy (QTE). The QTE method involves two main steps: (i) the quantile decomposition, and (ii) the detection of the nonlinear information transfer. It is a more generalized case of the symbolic transfer entropy (STE), which can give many more details regarding to the information transfer induced by large events and small events. We design the Monte Carlo simulations, which verify the accuracy and the robustness of our new method. The stock price–volume relationship is revisited by the QTE method at low and high frequencies, where the information transfer is found to be heterogenous in emerging markets.