Title: A bootstrap test to detect prominent Granger-causalities across frequencies,
Abstract: Granger-causality in the frequency domain is an emerging tool to analyze the
causal relationship between two time series. We propose a bootstrap test on
unconditional and conditional Granger-causality spectra, as well as on their
difference, to catch particularly prominent causality cycles in relative terms.
In particular, we consider a stochastic process derived applying independently
the stationary bootstrap to the original series. Our null hypothesis is that
each causality or causality difference is equal to the median across
frequencies computed on that process. In this way, we are able to disambiguate
causalities which depart significantly from the median one obtained ignoring
the causality structure. Our test shows power one as the process tends to
non-stationarity, thus being more conservative than parametric alternatives. As
an example, we infer about the relationship between money stock and GDP in the
Euro Area via our approach, considering inflation, unemployment and interest
rates as conditioning variables. We point out that during the period 1999-2017
the money stock aggregate M1 had a significant impact on economic output at all
frequencies, while the opposite relationship is significant only at high
frequencies.