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The decomposition and measurement of the interdependency between second-order stationary processes
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  • Published: December 1991

The decomposition and measurement of the interdependency between second-order stationary processes

  • Yuzo Hosoya1 

Probability Theory and Related Fields volume 88, pages 429–444 (1991)Cite this article

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  • 222 Citations

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Summary

For a given pair of multivariate stationary processes, the process of one-way effect is extracted from each of the processes. Each process is decomposed into two orthogonal processes, namely, into the process generated by the one-way effect of the other process and the process orthogonal to it. Based on the decomposition, three measures characterizing the interdependency of the pair of processes are introduced. They are the measure of association, the measure of one-way effect and the measure of reciprocity. Each of the measures is defined as overall as well as frequencywise measure. The paper shows that the measure of association is equal to the sum of the others. It discusses the relationships of those measures to the ones proposed by Gel'fand-Yaglom and by Geweke.

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Author information

Authors and Affiliations

  1. Faculty of Economics, Tohoku University, Kawauchi, 980, Sendai, Japan

    Yuzo Hosoya

Authors
  1. Yuzo Hosoya
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Additional information

This paper is partially supported by the Japanese Ministry of Education Grant for Scientific Research No. C02630010

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Cite this article

Hosoya, Y. The decomposition and measurement of the interdependency between second-order stationary processes. Probab. Th. Rel. Fields 88, 429–444 (1991). https://doi.org/10.1007/BF01192551

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  • Received: 25 June 1990

  • Revised: 02 November 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01192551

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Keywords

  • Stochastic Process
  • Stationary Process
  • Probability Theory
  • Mathematical Biology
  • Orthogonal Process
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