---
_id: '14446'
abstract:
- lang: eng
  text: 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.
acknowledgement: 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.
article_processing_charge: Yes
article_type: original
author:
- first_name: Jozef
  full_name: Jakubík, Jozef
  last_name: Jakubík
- first_name: Phuong
  full_name: Bui Thi Mai, Phuong
  id: 3EC6EE64-F248-11E8-B48F-1D18A9856A87
  last_name: Bui Thi Mai
- first_name: Martina
  full_name: Chvosteková, Martina
  last_name: Chvosteková
- first_name: Anna
  full_name: Krakovská, Anna
  last_name: Krakovská
citation:
  ama: Jakubík J, Phuong M, Chvosteková M, Krakovská A. Against the flow of time with
    multi-output models. <i>Measurement Science Review</i>. 2023;23(4):175-183. doi:<a
    href="https://doi.org/10.2478/msr-2023-0023">10.2478/msr-2023-0023</a>
  apa: Jakubík, J., Phuong, M., Chvosteková, M., &#38; Krakovská, A. (2023). Against
    the flow of time with multi-output models. <i>Measurement Science Review</i>.
    Sciendo. <a href="https://doi.org/10.2478/msr-2023-0023">https://doi.org/10.2478/msr-2023-0023</a>
  chicago: Jakubík, Jozef, Mary Phuong, Martina Chvosteková, and Anna Krakovská. “Against
    the Flow of Time with Multi-Output Models.” <i>Measurement Science Review</i>.
    Sciendo, 2023. <a href="https://doi.org/10.2478/msr-2023-0023">https://doi.org/10.2478/msr-2023-0023</a>.
  ieee: J. Jakubík, M. Phuong, M. Chvosteková, and A. Krakovská, “Against the flow
    of time with multi-output models,” <i>Measurement Science Review</i>, vol. 23,
    no. 4. Sciendo, pp. 175–183, 2023.
  ista: 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.
  mla: Jakubík, Jozef, et al. “Against the Flow of Time with Multi-Output Models.”
    <i>Measurement Science Review</i>, vol. 23, no. 4, Sciendo, 2023, pp. 175–83,
    doi:<a href="https://doi.org/10.2478/msr-2023-0023">10.2478/msr-2023-0023</a>.
  short: J. Jakubík, M. Phuong, M. Chvosteková, A. Krakovská, Measurement Science
    Review 23 (2023) 175–183.
date_created: 2023-10-22T22:01:15Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-09-09T13:10:30Z
day: '01'
ddc:
- '510'
department:
- _id: ChLa
doi: 10.2478/msr-2023-0023
external_id:
  isi:
  - '001070829600005'
file:
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  date_created: 2023-10-31T12:07:23Z
  date_updated: 2023-10-31T12:07:23Z
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file_date_updated: 2023-10-31T12:07:23Z
has_accepted_license: '1'
intvolume: '        23'
isi: 1
issue: '4'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 175-183
publication: Measurement Science Review
publication_identifier:
  eissn:
  - 1335-8871
publication_status: published
publisher: Sciendo
quality_controlled: '1'
scopus_import: '1'
status: public
title: Against the flow of time with multi-output models
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
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  short: CC BY-NC-ND (4.0)
type: journal_article
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volume: 23
year: '2023'
...