Bivariate temporal orders for causal inference
Causality analysis may be carried out at different levels of detail, e.g. parameter- or temporal-based (both in a global sense). There is hence a need for a local, more distinctive approach, particularly when analyzing data segments. Therefore, the bivariate temporal orders (BTO) estimation was introduced. It uses both "statistical" and "causal" approaches, with two different kernels in each (linear modeling and time series distance calculation, for statistical one; and entropy- and integral-approximation-based information geometric causal inference, for causal one). The algorithm was tested on cardiorespiratory data comprising tidal volume and tachogram curves, obtained from elite athletes (supine and standing, static conditions) and a control group (different rates and depths of breathing, while supine). BTO enables to find the local curves of the most optimal shifts between signals (causal vector) and to determine causally stable segments across time. In this context, the causal vectors were determined concerning body position and breathing style changes. The rate of breathing had a greater impact on the causal vector average than does the depth of breathing. The tachogram curve preceded the tidal volume more when breathing was slower. The stability was the highest for the highest breathing rate. The method is implemented in the provided R package and can be also used for other physiological studies or even different research areas.