Path Signature Area-Based Causal Discovery in Coupled Time Series
- URL: http://arxiv.org/abs/2110.12288v1
- Date: Sat, 23 Oct 2021 19:57:22 GMT
- Title: Path Signature Area-Based Causal Discovery in Coupled Time Series
- Authors: Will Glad and Thomas Woolf
- Abstract summary: We propose the application of confidence sequences to analyze the significance of the magnitude of the signed area between two variables.
This approach provides a new way to define the confidence of a causal link existing between two time series.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Coupled dynamical systems are frequently observed in nature, but often not
well understood in terms of their causal structure without additional domain
knowledge about the system. Especially when analyzing observational time series
data of dynamical systems where it is not possible to conduct controlled
experiments, for example time series of climate variables, it can be
challenging to determine how features causally influence each other. There are
many techniques available to recover causal relationships from data, such as
Granger causality, convergent cross mapping, and causal graph structure
learning approaches such as PCMCI. Path signatures and their associated signed
areas provide a new way to approach the analysis of causally linked dynamical
systems, particularly in informing a model-free, data-driven approach to
algorithmic causal discovery. With this paper, we explore the use of path
signatures in causal discovery and propose the application of confidence
sequences to analyze the significance of the magnitude of the signed area
between two variables. These confidence sequence regions converge with greater
sampling length, and in conjunction with analyzing pairwise signed areas across
time-shifted versions of the time series, can help identify the presence of
lag/lead causal relationships. This approach provides a new way to define the
confidence of a causal link existing between two time series, and ultimately
may provide a framework for hypothesis testing to define whether one time
series causes another
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