Measuring and testing Granger causality over the spectrum: An application to European production expectation surveys

Decomposing Granger causality over the spectrum allows us to disentangle potentially different Granger causality relationships over different frequencies. This may yield new and complementary insights compared to traditional versions of Granger causality. In this paper, we compare two existing approaches in the frequency domain, proposed originally by Pierce [Pierce, D. A. (1979). R-squared measures for time series. Journal of the American Statistical Association, 74, 901–910] and Geweke [Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77, 304–324], and introduce a new testing procedure for the Pierce spectral Granger causality measure. To provide insights into the relative performance of this test, we study its power properties by means of Monte Carlo simulations. In addition, we apply the methodology in the context of the predictive value of the European production expectation surveys. This predictive content is found to vary widely with the frequency considered, illustrating the usefulness of not restricting oneself to a single overall test statistic.