Tests Of Non-Causality In A Frequency Band

We extend the frequency-specific Granger-causality test of Breitung and Candelon (2006) to a more general null hypothesis that allows non-causality at unknown frequencies within an interval, instead of having to prespecify a single frequency. This setup corresponds better to most hypotheses that are typically analyzed in applied research and is easy to implement. We also discuss a test approach that departs from strict non-causality, given the impossibility of (non-trivial) non-causality over a continuum of frequencies. In an empirical application dealing with the dynamics of US temperatures and CO2 emissions we find that emissions cause temperature changes only at very low frequencies with more than 30 years of oscillation.