Time-Domain and Spectral Decomposition of Dynamic Coupling with Instantaneous and Time-Lagged Causality: Methodological Evaluation and Application to Cardiovascular Variability
Abstract
The quantification of dynamic interactions in coupled physiological time series is a central question in biomedical signal processing. A critical issue is the presence of instantaneous dependencies, often neglected in conventional Granger causality (GC) analyses despite potentially reflecting physiologically meaningful effects. We investigate time- and frequency-domain measures of causality within the linear autoregressive (AR) framework, treating instantaneous dependencies according to three formulations: (i) the classical strictly causal AR model, providing spectral measures of time-lagged GC and instantaneous interaction; (ii) the Geweke approach, assigning instantaneous dependencies to the direction opposite to that under investigation; (iii) a single extended AR model incorporating causally-oriented instantaneous dependencies, yielding spectral GC measures accounting for both instantaneous and time-lagged causality. The three approaches are evaluated in simulated Gaussian systems, where dynamic measures can be derived analytically and compared with the expected coupling structure. The single extended AR model emerges as the most consistent formulation when instantaneous dependencies have a physiologically meaningful causal direction and is then applied to cardiovascular interactions between heart period (HP) and systolic (SAP) or diastolic arterial pressure (DAP) in healthy subjects during postural and mental stress. Accounting for instantaneous dependencies substantially affects HP-SAP and HP-DAP interactions, enabling better quantification of baroreflex and cardiac run-off mechanisms and characterization of their responses to stress and of low- and high-frequency dynamics. Overall, the framework provides consistent representation of causal interactions across time and frequency and highlights the importance of accounting for instantaneous dependencies in physiological coupling.
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BibTeX
@misc{mijatovic2026timedomain,
title = {{Time-Domain and Spectral Decomposition of Dynamic Coupling with Instantaneous and Time-Lagged Causality: Methodological Evaluation and Application to Cardiovascular Variability}},
author = {Gorana Mijatovic and Marta Iovino and Michal Javorka and Luca Faes},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.14531},
eprint = {2611.14531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.14531},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-Domain and Spectral Decomposition of Dynamic Coupling with Instantaneous and Time-Lagged Causality: Methodological Evaluation and Application to Cardiovascular Variability
AU - Gorana Mijatovic
AU - Marta Iovino
AU - Michal Javorka
AU - Luca Faes
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.14531
UR - https://arxiv.org/abs/2611.14531
AB - The quantification of dynamic interactions in coupled physiological time series is a central question in biomedical signal processing. A critical issue is the presence of instantaneous dependencies, often neglected in conventional Granger causality (GC) analyses despite potentially reflecting physiologically meaningful effects. We investigate time- and frequency-domain measures of causality within the linear autoregressive (AR) framework, treating instantaneous dependencies according to three formulations: (i) the classical strictly causal AR model, providing spectral measures of time-lagged GC and instantaneous interaction; (ii) the Geweke approach, assigning instantaneous dependencies to the direction opposite to that under investigation; (iii) a single extended AR model incorporating causally-oriented instantaneous dependencies, yielding spectral GC measures accounting for both instantaneous and time-lagged causality. The three approaches are evaluated in simulated Gaussian systems, where dynamic measures can be derived analytically and compared with the expected coupling structure. The single extended AR model emerges as the most consistent formulation when instantaneous dependencies have a physiologically meaningful causal direction and is then applied to cardiovascular interactions between heart period (HP) and systolic (SAP) or diastolic arterial pressure (DAP) in healthy subjects during postural and mental stress. Accounting for instantaneous dependencies substantially affects HP-SAP and HP-DAP interactions, enabling better quantification of baroreflex and cardiac run-off mechanisms and characterization of their responses to stress and of low- and high-frequency dynamics. Overall, the framework provides consistent representation of causal interactions across time and frequency and highlights the importance of accounting for instantaneous dependencies in physiological coupling.
ER -