On the Sensitivity of Granger Causality to Errors‐In‐Variables, Linear Transformations and Subsampling

Anderson, Brian D.O.; Deistler, Manfred and Dufour, Jean-Marie (2019) On the Sensitivity of Granger Causality to Errors‐In‐Variables, Linear Transformations and Subsampling. Journal of Time Series Analysis, 40 (1), pp. 102-123. DOI: 10.1111/jtsa.12430

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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.

Item Type: Article in Academic Journal
Keywords: Granger causality, sensitivity, signal‐to‐noise ratio, errors‐in‐variables, measurement errors, filtering, subsampling
Research Units: Current Research Groups > IHS general publications
Date Deposited: 09 Oct 2018 08:26
Last Modified: 20 Feb 2019 13:26
DOI: 10.1111/jtsa.12430
ISSN: 0143-9782
URI: https://irihs.ihs.ac.at/id/eprint/4788

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