Dynamic Window-level Granger Causality of Multi-channel Time Series
Abstract: Granger causality (GC) techniques facilitate the examination of temporal causal relationships by assessing the predictive utility of one time series for another. However, conventional GC approaches are limited to linear scenarios and assume that causalities exclusively exist between entire time series channels, remaining constant over time. This assumption falls short when dealing with real-world time series data characterized by dynamic causalities among channels. To address this limitation, we present the dynamic window-level Granger causality with causality index (DWGC-CI) method, which incorporates nonlinear window-level variability into the traditional GC framework. The DWGC-CI method specifically employs F-tests on sliding windows to assess forecasting errors, subsequently extracting dynamic causalities using a causality index. This index involves the introduction of a negative feedback adjustment mechanism, which mitigates window-level noisy fluctuations and helps extract dynamic causalities. We theoretically demonstrate that, compared to traditional channel-level GC methods, DWGC-CI accurately captures window-level GCs. In experimental evaluations involving two synthetic datasets, DWGC-CI significantly surpasses the baseline in terms of accuracy and recall rates. Furthermore, when applied to two real-world datasets, DWGC-CI effectively identifies seasonal and annual varying GCs, demonstrating a markedly better consistency with domain-specific knowledge of seasonal meteorology and stock market dynamics.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: The revised draft has been uploaded. We sincerely appreciate the suggestions provided by everyone and have made improvements in the revised version one by one accordingly. Specifically, our modifications are as follows:
**1)** In the method section, we further emphasize the differences between DWGC-CI and DWGC in terms of assumptions and preset tasks (RW1). We also provide a more specific explanation of the composition of the CI matrix and $L_{index}$, as well as their differences and advantages compared to traditional methods such as change-point detection and parameter smoothing (RW1,2,3, Appendix).
**2)** In the theoretical part, we explain the motivation behind Theorem 1 and further move the theorem hypothesis to the main text (RW1). We also provide a detailed explanation of the assumptions (RW3, Appendix).
**3)** In the experimental part, we made our best efforts to collect additional work as baselines to demonstrate the superiority of our method (RW1,2,3). These experiments specifically include:
**3-1)** More comprehensive experiments on the original task, including variance robustness analysis and more detailed result explanations (RW1,2,3);
**3-2)** Extension of the two-channel approach to multi-channel (RW2, Appendix);
**3-3)** Other auxiliary analyses: **a)** Experimental comparison of the effectiveness of CI updating on causal windows and all windows (RW1), **b)** sensitivity testing of the $\alpha$ parameter in $L_{index}$ (RW1), and **c)** the impact of insufficient NAR training on experimental results (RW2).
**4)** Other typos.
Once again, we express our sincere gratitude! Discussions are always welcomed.
Assigned Action Editor: ~Mingming_Gong1
Submission Number: 1427
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