Measurement of Linear Dependence and Feedback between Multiple Time Series

TLDR

The paper defines measures of linear dependence and feedback for multiple time series, expressing dependence as the sum of bidirectional linear feedback and instantaneous feedback, and shows these feedback components can be additively decomposed by frequency. A concise inference theory for these measures and their frequency decompositions is presented, with modest computational requirements. The measures are nonnegative and equal zero only when the corresponding feedback (causality) is absent. Keywords: multiple time series, feedback, dependence, causality.

Abstract

Abstract Measures of linear dependence and feedback for multiple time series are defined. The measure of linear dependence is the sum of the measure of linear feedback from the first series to the second, linear feedback from the second to the first, and instantaneous linear feedback. The measures are nonnegative, and zero only when feedback (causality) of the relevant type is absent. The measures of linear feedback from one series to another can be additively decomposed by frequency. A readily usable theory of inference for all of these measures and their decompositions is described; the computations involved are modest. Key Words: Multiple time scriesFeedbackDependenceCausality