On the causality between multiple locally stationary processes
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 \(\lambda\).
scientific article; zbMATH DE number 6065402