The Measures of One-Way Effect, Reciprocity, and Association

Abstract

To characterize the interdependent structure of a pair of two jointly second-order stationary processes , this chapter introduces the (overall as well as frequency-wise) measures of one-way effect, reciprocity, and association. Section 2.2 defines the Granger and Sims non-causality and establishes their equivalence for a general class of (not necessarily stationary) second-order processes. Sections 2.3 and 2.4 define the overall and frequency-wise one-way effect measures and provide three ways of deriving the frequency-wise measure. One is based on direct canonical factorization of the spectral density matrix. The other two are based on distributed-lag representation and innovation orthogonalization, respectively. Each approach provides a different representation of the same quantity. Section 2.5 introduces the overall and the frequency-wise measures of reciprocity and association.