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

  • Yuzo HosoyaEmail author
  • Kosuke Oya
  • Taro Takimoto
  • Ryo Kinoshita
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


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.


Canonical factorization Frequency-domain representation Granger non-causality Measure of association Measure of one-way effect Measure of reciprocity Prediction improvement Purely reciprocal component process Sims non-causality 


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Yuzo Hosoya
    • 1
    Email author
  • Kosuke Oya
    • 2
  • Taro Takimoto
    • 3
  • Ryo Kinoshita
    • 4
  1. 1.Tohoku UniversitySendaiJapan
  2. 2.Osaka UniversityToyonakaJapan
  3. 3.Kyushu UniversityFukuokaJapan
  4. 4.Tokyo Keizai UniversityKokubunjiJapan

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