fastC-GC and fastC-GC*: Efficient RCCP-Guided Graph Estimation for Time Series
Abstract
We introduce fastC-GC and fastC-GC*, computationally efficient methods for time-series graph estimation using the two-test rule motivated by Reichenbach's common cause principle (RCCP) and the conditioning sets of causalised Granger causality (c-GC and c-GC*). The methods use standardized data, ridge-residual correlation, and complete circular shift enumeration evaluated by Fourier transforms. Shared precision calculations and Schur downdates avoid repeated regression fits. On a single-threaded benchmark, fastC-GC was 68-277 times faster than the compared c-GC implementation, and fastC-GC* was 192-886 times faster than c-GC*. Across four suites with reference graphs, aggregate mean area under the precision-recall curve (AUPRC) differed from the corresponding baseline by at most 0.019, but F1 was lower at the selected thresholds in every suite. The computational gains therefore accompany a change in estimator and selected graphs. Among eight methods, Bagged PCMCI+ had the highest mean AUPRC on sparse VAR, an autocorrelated structural process, and DREAM3; CUTS+ led on Lorenz-96. Wind-tunnel and river-discharge applications illustrate differences between inferred graphs without establishing causal accuracy. We prove the computational identities and a restricted population adjacency result for fastC-GC*. Causal interpretation requires the stated graphical assumptions; validity of the implemented tests additionally requires a suitable shift-invariant null law. Empirical null rejection rates informed the conditional threshold β= 0.005, without establishing general test validity or graph-wide error control.
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BibTeX
@misc{adedayo2026fastcgc,
title = {{fastC-GC and fastC-GC*: Efficient RCCP-Guided Graph Estimation for Time Series}},
author = {S. A. Adedayo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37883},
eprint = {2610.37883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - fastC-GC and fastC-GC*: Efficient RCCP-Guided Graph Estimation for Time Series
AU - S. A. Adedayo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37883
UR - https://arxiv.org/abs/2610.37883
AB - We introduce fastC-GC and fastC-GC^*, computationally efficient methods for time-series graph estimation using the two-test rule motivated by Reichenbach's common cause principle (RCCP) and the conditioning sets of causalised Granger causality (c-GC and c-GC^*). The methods use standardized data, ridge-residual correlation, and complete circular shift enumeration evaluated by Fourier transforms. Shared precision calculations and Schur downdates avoid repeated regression fits. On a single-threaded benchmark, fastC-GC was 68-277 times faster than the compared c-GC implementation, and fastC-GC^* was 192-886 times faster than c-GC^*. Across four suites with reference graphs, aggregate mean area under the precision-recall curve (AUPRC) differed from the corresponding baseline by at most 0.019, but F1 was lower at the selected thresholds in every suite. The computational gains therefore accompany a change in estimator and selected graphs. Among eight methods, Bagged PCMCI+ had the highest mean AUPRC on sparse VAR, an autocorrelated structural process, and DREAM3; CUTS+ led on Lorenz-96. Wind-tunnel and river-discharge applications illustrate differences between inferred graphs without establishing causal accuracy. We prove the computational identities and a restricted population adjacency result for fastC-GC^*. Causal interpretation requires the stated graphical assumptions; validity of the implemented tests additionally requires a suitable shift-invariant null law. Empirical null rejection rates informed the conditional threshold β= 0.005, without establishing general test validity or graph-wide error control.
ER -