A Bootstrap Method to Test Granger-Causality in the Frequency Domain

We propose a bootstrap test for unconditional and conditional Granger-causality spectra in the frequency domain. Our test aims to detect if the causality at a particular frequency is systematically different from zero. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. At each frequency, we test the sample causality against the distribution of the median causality across frequencies estimated for that process. Via our procedure, we infer about the relationship between money stock and GDP in the Euro Area during the period 1999-2017. We point out that the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at low frequencies.