A time-series analysis method based on the directed transinformation

In a previous paper we presented procedures of analyzing causality between a time series based on information theory and information flow between time series based on a concept of directed transinformation, which is an information quantity with a direction. In principle, the directed transinformation is defined based on joint probability density between time series. As the length of the time series becomes larger, however, the volume of computation needed also increases exponentially. In this paper, we will discuss efficient computation algorithms. First, we assume Gaussian properties with the time series to present the “correlation function method” as a means of computing of the directed transinformation from correlation function. Second, we present a “linear production model method” in which the information quantity is computed by means of impulse response of a linear production model of the time series. Also, we proved that the linear production model can easily be composed by auto-regression if the time series is steady. Finally, we discussed the validity of time-series analysis based on the directed transinformation through analysis of an artificially produced simulated series. We have concluded that the proposed computation method can provide correct analysis even if the causality of the time series can not be analyzed correctly based on the correlation function.