On the causality between multiple locally stationary processes
type: Item
instance of: scholarly article
title: On the causality between multiple locally stationary processes
zbMATH Open document ID: 1247.60049
DOI: 10.1155/2012/261707
author: Junichi Hirukawa
published in: Advances in Decision Sciences
publication date: 2012-08-14T00:00:00Z
review text: Summary: When one would like to describe the relations between multivariate time series, the concepts of dependence and causality are of importance. These concepts also appear to be useful when one is describing the properties of an engineering or econometric model. Although the measures of dependence and causality under stationary assumption are well established, empirical studies show that these measures are not constant in time. Recently one of the most important classes of nonstationary processes has been formulated in a rigorous asymptotic framework by \textit{R. Dahlhaus} [Stochastic Processes Appl. 62, No. 1, 139--168 (1996; Zbl 0849.60032); Ann. Stat. 25, No. 1, 1--37 (1997; Zbl 0871.62080); Ann. Stat. 28, No. 6, 1762--1794 (2000; Zbl 1010.62078)], called locally stationary processes. Locally stationary processes have time-varying spectral densities whose spectral structures smoothly change in time. Here, we generalize measures of linear dependence and causality to multiple locally stationary processes. We give the measures of linear dependence, linear causality from one series to the other, and instantaneous linear feedback, at time \(t\) and frequency \(\lambda\).
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G12
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62M15
zbMATH DE Number: 6065402
zbMATH Keywords: concepts of dependence and causality
zbMATH Keywords: locally stationary processes
zbMATH Keywords: time-varying spectral densities
zbMATH Keywords: measures of linear dependence
Wikidata QID: Q58697762
MaRDI profile type: Publication
OpenAlex ID: W2077479335
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description: scientific article; zbMATH DE number 6065402