Elimination of Third‐series Effect and Defining Partial Measures of Causality

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Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG (2011, background): “As GC developed, the concept was generalized from bivariate to multivariate signals [21,22].”
Testing for short- and long-run causality: A frequency-domain approach (2006, methodology): “…C12ðLÞ C13ðLÞC21ðLÞ C22ðLÞ C23ðLÞ C31ðLÞ C32ðLÞ C33ðLÞ 264 375 Z1tZ2t Z3t 264 375, it follows that ut ¼ C11ðLÞZ1t þC12ðLÞZ2t and vt ¼ C21ðLÞZ1t þC22ðLÞZ2t: The causality measure suggested by Hosoya (2001) is equivalent to the bivariate causality measure between ut and vt My1!y2jy3 ðoÞ…”
Interpreting Euro Area Inflation at High and Low Frequencies (2008, unknown): “18 money growth and inflation on the residuals from a regression of the output gap and the interest rate change on lagged values of πt and μt.38 Hosoya (2000) shows that the causality measure from money growth to inflation, given the output gap and the interest rate change, is equal to the…”
Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. (2006, methodology): “Although Hosoya presented some improvements on Geweke’s methods (both bivariate (Hosoya, 1991) and conditional versions (Hosoya, 2001)), they have not been widely accepted because his time domain implementation departs from Granger’s original idea, and its physical interpretation is less clear.”