Measuring the Arrow of Time: Identification, Estimation, and Inference for Directional Structure in Multivariate Time Series
测量时间之箭:多元时间序列方向结构的识别、估计与推断
Many questions across the sciences take the same form: several coupled series are observed together, and the analyst wants to know not merely that they move together but which one moves first, and how strongly. This paper sets out a complete method built on one organising idea: the direction of a coupled system is exactly the part of its behaviour that changes when the record is played backwards. Tools built on contemporaneous covariance alone (correlation matrices, distance…