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On the Sensitivity of Granger Causality to Errors‐In‐Variables, Linear Transformations and Subsampling
Author(s) -
Anderson Brian D.O.,
Deistler Manfred,
Dufour JeanMarie
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12430
Subject(s) - granger causality , spurious relationship , mathematics , sensitivity (control systems) , causality (physics) , invertible matrix , econometrics , noise (video) , statistics , pure mathematics , computer science , artificial intelligence , physics , quantum mechanics , electronic engineering , engineering , image (mathematics)
This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger‐causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors‐in‐variables case, we give a continuity result, which implies that: a ‘small’ noise‐to‐signal ratio entails ‘small’ distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which ‘spurious’ causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches.