Testing for causality in real time

A framework for testing in real time (on-line) the statistical significance of the causality between nonstationary random processes is developed. The process representation is that of transfer function (TF-ARMA) models; the causality parameters are prediction error variances and dynamic multipliers; the estimation algorithm is that of recursive nonlinear least squares (RNLS). The basic step is made by analyzing the asymptotic distribution of this estimator under an assumption of stationary, but in operative conditions given by discounting past observations with exponential weights (EW). An empirical example, based on real economic time series, illustrates and checks the method of on-line inference.