Iterative causal discovery uncovers dynamic effects in wearable exercise data

Causal analysis of high-dimensional physiological time-series data is crucial for understanding the dynamic interactions among physical activity, metabolism, and heart rate. We present a sound and complete algorithm, called time-series iterative causal discovery (TS-ICD), for recovering partial ancestral graphs from high-dimensional physiological time-series data. Using the discovered causal structures, we perform mediation analysis to confirm the physiological validity of the identified relationships. We evaluate TS-ICD on both simulated datasets and a large-scale physiological monitoring dataset ( $$N = 330{,}842$$ ). The results show that TS-ICD reduces computational cost while recovering causal structures with strict temporal consistency and strong physiological interpretability. Additionally, this study identifies two key physiological pathways. First, we reveal a strong physiological memory effect of exercise intensity. Its indirect effect ( $$Effect = 11.582$$ ) accounts for 73% of the total effect, indicating that past exercise mainly affects current resting heart rate by keeping activity levels consistent and gradually building up over time. Second, we confirm that the effect of step count on heart rate is entirely through metabolic equivalents (METs). The direct effect of step count on heart rate is not significant ( $$p = 0.606$$ ), whereas the indirect effect through METs is highly significant ( $$Effect = 0.393$$ , 95% CI [0.389, 0.396]). These findings indicate that mechanical movement affects heart rate only when it generates sufficient metabolic demand. Overall, TS-ICD successfully recovers physiologically valid causal pathways and offers an efficient, interpretable framework for analyzing complex time-series data.