Jakubík, Jozef; Phuong, MaryISTA; Chvosteková, Martina; Krakovská, Anna
Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X → Y. The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal.
Measurement Science Review
The work was supported by the Scientific Grant Agency of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences, projects APVV-21-0216, VEGA2-0096-21 and VEGA 2-0023-22.
Jakubík J, Phuong M, Chvosteková M, Krakovská A. Against the flow of time with multi-output models. Measurement Science Review. 2023;23(4):175-183. doi:10.2478/msr-2023-0023
Jakubík, J., Phuong, M., Chvosteková, M., & Krakovská, A. (2023). Against the flow of time with multi-output models. Measurement Science Review. Sciendo. https://doi.org/10.2478/msr-2023-0023
Jakubík, Jozef, Mary Phuong, Martina Chvosteková, and Anna Krakovská. “Against the Flow of Time with Multi-Output Models.” Measurement Science Review. Sciendo, 2023. https://doi.org/10.2478/msr-2023-0023.
J. Jakubík, M. Phuong, M. Chvosteková, and A. Krakovská, “Against the flow of time with multi-output models,” Measurement Science Review, vol. 23, no. 4. Sciendo, pp. 175–183, 2023.
Jakubík J, Phuong M, Chvosteková M, Krakovská A. 2023. Against the flow of time with multi-output models. Measurement Science Review. 23(4), 175–183.
Jakubík, Jozef, et al. “Against the Flow of Time with Multi-Output Models.” Measurement Science Review, vol. 23, no. 4, Sciendo, 2023, pp. 175–83, doi:10.2478/msr-2023-0023.
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