A macroeconomic time series is usually described by an autoregressive moving average process which contains a unit root(called integrated) or a trend component. This paper demonstrates that standard Granger causality test often leads to spurious causality between two independent autoregressive movingaverage processes in which both of them are integrated processes,especially one of them is an integrated process and the other is atrend stationary process. The asymptotic distributions of F statistics for testing Granger causality convergetonon-standarddistributions for two integrated processes, but diverge at a Trate for an integrated process and a trend stationaryprocess.

spurious Granger causality, hypothesis test, asymptotic distribution, functional of Brownian motion, unit root,trend stationary.