Characterizing Interdependencies of Multiple Time Series

Theory and Applications

  • Yuzo Hosoya
  • Kosuke Oya
  • Taro Takimoto
  • Ryo Kinoshita

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Also part of the JSS Research Series in Statistics book sub series (JSSRES)

Table of contents

  1. Front Matter
    Pages i-x
  2. Yuzo Hosoya, Kosuke Oya, Taro Takimoto, Ryo Kinoshita
    Pages 1-19
  3. Yuzo Hosoya, Kosuke Oya, Taro Takimoto, Ryo Kinoshita
    Pages 21-43
  4. Yuzo Hosoya, Kosuke Oya, Taro Takimoto, Ryo Kinoshita
    Pages 45-64
  5. Yuzo Hosoya, Kosuke Oya, Taro Takimoto, Ryo Kinoshita
    Pages 65-102
  6. Yuzo Hosoya, Kosuke Oya, Taro Takimoto, Ryo Kinoshita
    Pages 103-122
  7. Back Matter
    Pages 123-133

About this book


This book introduces academic researchers and professionals to the basic concepts and methods for characterizing interdependencies of multiple time series in the frequency domain. Detecting causal directions between a pair of time series and the extent of their effects, as well as testing the non existence of a feedback relation between them, have constituted major focal points in multiple time series analysis since Granger introduced the celebrated definition of causality in view of prediction improvement.

Causality analysis has since been widely applied in many disciplines. Although most analyses are conducted from the perspective of the time domain, a frequency domain method introduced in this book sheds new light on another aspect that disentangles the interdependencies between multiple time series in terms of long-term or short-term effects, quantitatively characterizing them. The frequency domain method includes the Granger noncausality test as a special case.

Chapters 2 and 3 of the book introduce an improved version of the basic concepts for measuring the one-way effect, reciprocity, and association of multiple time series, which were originally proposed by Hosoya. Then the statistical inferences of these measures are presented, with a focus on the stationary multivariate autoregressive moving-average processes, which include the estimation and test of causality change. Empirical analyses are provided to illustrate what alternative aspects are detected and how the methods introduced here can be conveniently applied. Most of the materials in Chapters 4 and 5 are based on the authors' latest research work. Subsidiary items are collected in the Appendix.


Autoregressive Moving-average Model Canonical Factorization Causal Analysis Large Sample Test Prediction Error

Authors and affiliations

  • Yuzo Hosoya
    • 1
  • 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

Bibliographic information