GRANGERSPEC: Stata module to Granger causality tests across frequencies: Granger-causality spectra

grangerspec provides seven tools for Granger causality in the frequency domain. All series must be stationary, I(0): the spectra and every test are built on stationary-VAR representations, and a stable VAR (every companion root modulus below one) is assumed. Difference or detrend integrated series first - the article's own application passes all six series through the Hodrick-Prescott filter before testing - and check the Stability line of the output. Time-domain Granger causality only says whether the past of a series y helps predict a series x overall. The frequency-domain Granger-causality spectrum of Geweke (1982, 1984) instead measures the strength of the causal link at each frequency, so that causality at low (business-cycle) and high frequencies can be distinguished. Inference on these spectra, however, is an open problem: the limiting distribution of the estimated spectrum under the null of no causality is unknown (Farne and Montanari 2022, Section 2.2). Farne and Montanari propose a bootstrap solution: they test each frequency-specific causality against the distribution of the median causality across frequencies computed on stationary-bootstrap series that are independent by construction, so that the null hypothesis is stochastic independence between the series. grangerspec computes the spectra and performs this bootstrap test.