Abstract
This work is about observational causal discovery for deterministic and stochastic dynamic systems. We explore what additional knowledge can be gained by the usage of standard conditional independence tests and if the interacting systems are located in a geodesic space.
Highlights
It is not necessary to emphasize the importance of the concept of causality in science and in the natural sciences in particular
A new approach was presented in a recent work [11] that was based on the comparison of the dimension of the attractors of the given systems and their joint observation
The present paper investigates the causal relation of a pair of dynamic systems
Summary
It is not necessary to emphasize the importance of the concept of causality in science and in the natural sciences in particular. Revealing causal relations between systems via the time series produced by them is one of the most attractive challenges. It is not able to detect hidden common cause and, instead, indicates false directional causal relation between the observed systems (for details of all the pros and cons cf [3]). Stark [9,10] generalized Takens’ result and showed the theoretical limitations to use it for stochastic dynamic systems. The present paper investigates the causal relation of a pair of dynamic systems (which might be deterministic or stochastic). Our aim is to find the causal relationship between two stochastic dynamic systems X and Y from which we observe the time series {xi}in=1, {yi}in=1. (It is a SVAR(d, p) process, were d is the multi index of dimensions of the variables, and p is the order of auto-regression.).
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