  Constraint-based methods and noise-based methods are two distinct families of
methods proposed for uncovering causal graphs from observational data. However,
both operate under strong assumptions that may be challenging to validate or
could be violated in real-world scenarios. In response to these challenges,
there is a growing interest in hybrid methods that amalgamate principles from
both methods, showing robustness to assumption violations. This paper
introduces a novel comprehensive framework for hybridizing constraint-based and
noise-based methods designed to uncover causal graphs from observational time
series. The framework is structured into two classes. The first class employs a
noise-based strategy to identify a super graph, containing the true graph,
followed by a constraint-based strategy to eliminate unnecessary edges. In the
second class, a constraint-based strategy is applied to identify a skeleton,
which is then oriented using a noise-based strategy. The paper provides
theoretical guarantees for each class under the condition that all assumptions
are satisfied, and it outlines some properties when assumptions are violated.
To validate the efficacy of the framework, two algorithms from each class are
experimentally tested on simulated data, realistic ecological data, and real
datasets sourced from diverse applications. Notably, two novel datasets related
to Information Technology monitoring are introduced within the set of
considered real datasets. The experimental results underscore the robustness
and effectiveness of the hybrid approaches across a broad spectrum of datasets.
