Inferring Granger-Causality Among Cyclostationary Time Series Through Time-invariant Estimators

Analyzing the causal interplay among a number of dynamic systems is a problem encountered in many applications across various disciplines. Given a family of time series, the objective is to determine whether one process is influenced by the others. Interdependence relations among wide-sense-stationary (WSS) sequences can be formally analyzed using Granger-causality as a tool. However, many processes encountered in practice are non-stationary and are described by parameters that change periodically with time. In this paper, it is shown that useful information on the Granger-causality between two cyclostationary (CS) time series can be obtained simply by treating the processes as WSS, without a consideration of the periodic nature of the parameters or the exact knowledge of the period of cyclostationarity. Furthermore, we demonstrate the use of time-invariant multivariate autoregressive (MVAR) estimators and Wiener filters in detecting Granger-causality among a number of CS time series.