On the Causality between Multiple Locally Stationary Processes. (30th May 2012)

• Record Type: Journal Article
• Authors: Hirukawa, Junichi
• Other Names: Tamaki Kenichiro Academic Editor.
• Is Part Of: Advances in decision sciences. Volume 2012(2012)
• Publication Date: 2012-05-30
• Subjects: Decision making -- Periodicals; Decision making; Electronic journals; Periodicals; 519
• DOI: 10.1155/2012/261707
• Languages: English
• ISSNs: 2090-3359

Abstract

Abstract : 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 Dahlhaus in (1996), (1997), and (2000), 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 λ .