Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction
Abstract
:1. Introduction
2. An Overview of the Theory of Information Flow-Based Causality Analysis
2.1. Directed Graph, Uncertainty Propagation, and Causality
2.2. A Brief Stroll through the Theory and Recent Advances
If the evolution of an event, say, , is independent of another one, , then the information flow from to is zero.
3. Information Flow among Time Series and Algorithm for Multivariate Causal Inference
Algorithm 1: Quantitative causal inference |
Input : d time series Output: a DG , and IFs along edges initialize such that all vertexes are isolated; set a significance level ; for each do compute by (14); if is significant at level then add to ; record ; end end return , together with the IFs |
4. Normalization of the Causality among Multivariate Time Series
5. Application to Causal Graph Reconstruction
5.1. A Noisy Causal Network from Autoregressive Processes
5.2. A Network of Nearly Synchronized Chaotic Series
6. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
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Liang, X.S. Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction. Entropy 2021, 23, 679. https://doi.org/10.3390/e23060679
Liang XS. Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction. Entropy. 2021; 23(6):679. https://doi.org/10.3390/e23060679
Chicago/Turabian StyleLiang, X. San. 2021. "Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction" Entropy 23, no. 6: 679. https://doi.org/10.3390/e23060679