Granger Causality on forward and Reversed Time Series
Institute of Measurement Science, Slovak Academy of Sciences, 84104 Bratislava, Slovakia
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Academic Editor: Philip Broadbridge
Entropy 2021, 23(4), 409; https://doi.org/10.3390/e23040409
Received: 31 January 2021
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Revised: 24 March 2021
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Accepted: 27 March 2021
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Published: 30 March 2021
(This article belongs to the Special Issue Information Transfer, Entropy Production, Irreversibility and Time Series Analysis)
In this study, the information flow time arrow is investigated for stochastic data defined by vector autoregressive models. The time series are analyzed forward and backward by different Granger causality detection methods. Besides the normal distribution, which is usually required for the validity of Granger causality analysis, several other distributions of predictive errors are considered. A clear effect of a change in the order of cause and effect on the time-reversed series of unidirectionally connected variables was detected with standard Granger causality test (GC), when the product of the connection strength and the ratio of the predictive errors of the driver and the recipient was below a certain level, otherwise bidirectional causal connection was detected. On the other hand, opposite causal link was detected unconditionally by the methods based on the time reversal testing, but they were not able to detect correct bidirectional connection. The usefulness of the backward analysis is manifested in cases where falsely detected unidirectional connections can be rejected by applying the result obtained after the time reversal, and in cases of uncorrelated causally independent variables, where the absence of a causal link detected by GC on the original series should be confirmed on the time-reversed series.
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Keywords:
time reversal; Granger causality; predictive error; endogeneity
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MDPI and ACS Style
Chvosteková, M.; Jakubík, J.; Krakovská, A. Granger Causality on forward and Reversed Time Series. Entropy 2021, 23, 409. https://doi.org/10.3390/e23040409
AMA Style
Chvosteková M, Jakubík J, Krakovská A. Granger Causality on forward and Reversed Time Series. Entropy. 2021; 23(4):409. https://doi.org/10.3390/e23040409
Chicago/Turabian StyleChvosteková, Martina, Jozef Jakubík, and Anna Krakovská. 2021. "Granger Causality on forward and Reversed Time Series" Entropy 23, no. 4: 409. https://doi.org/10.3390/e23040409
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