# Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions

## TL;DR

This paper establishes theoretical conditions under which micro-level causal edges in time series can be oriented using summary causal graphs and faithful distributions, aiding causal discovery in complex temporal systems.

## Contribution

It provides the first formal conditions for orienting micro-level causal edges from macro-level summaries and faithful distributions, even with cycles or bidirected edges.

## Key findings

- Guarantees for edge orientation at the micro-level
- Conditions applicable to cyclic and bidirected macro-level graphs
- Guidance for causal inference using summary causal graphs

## Abstract

Understanding causal relations between temporal variables is a central challenge in time series analysis, particularly when the full causal structure is unknown. Even when the full causal structure cannot be fully specified, experts often succeed in providing a high-level abstraction of the causal graph, known as a summary causal graph, which captures the main causal relations between different time series while abstracting away micro-level details. In this work, we present conditions that guarantee the orientability of micro-level edges between temporal variables given the background knowledge encoded in a summary causal graph and assuming having access to a faithful and causally sufficient distribution with respect to the true unknown graph. Our results provide theoretical guarantees for edge orientation at the micro-level, even in the presence of cycles or bidirected edges at the macro-level. These findings offer practical guidance for leveraging SCGs to inform causal discovery in complex temporal systems and highlight the value of incorporating expert knowledge to improve causal inference from observational time series data.