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Conditional Independence Testing in Time Series — arXiv:2609.20772

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.20772
License (as archived): CC0-1.0
Archived: 2026-10-10T04:19:36.750Z
SHA-256 of the archived text: 718c07d93f3bd84830e875e62c42c4c48a3f43df9f6381cd56174531e2a841ed
Stable URL of this page: https://metraipolis.com/documento/dc_935a139bb29c

How to cite

Conditional Independence Testing in Time Series — arXiv:2609.20772 — arXiv (en), https://arxiv.org/abs/2609.20772 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_935a139bb29c (Metraipolis archive dc_935a139bb29c, sha256 718c07d93f3bd84830e875e62c42c4c48a3f43df9f6381cd56174531e2a841ed)

BibTeX

@misc{dc935a139bb29c,
  title = {Conditional Independence Testing in Time Series — arXiv:2609.20772},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.20772},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_935a139bb29c; sha256 718c07d93f3bd84830e875e62c42c4c48a3f43df9f6381cd56174531e2a841ed},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.20772. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects from associations driven by common external processes, supporting reliable decision-makings in applications such as finance, neuroscience, and climate science. While traditional approaches assume a linear vector autoregressive (VAR) model and are vulnerable to misspecification, we instead address a model-free version of the problem. We propose nonlinearly regressing both the outcome and exposure on the joint history of $Y$ and $Z$, and calculating a test statistic based on the sample covariance of residuals, we call the Generalised Temporal Covariance Measure (GTCM). To account for heteroscedasticity and improve power against local alternatives, we incorporate variance weights and employ a data-adaptive test based on polynomial lag this http URL type I error control of the test relies on the relatively weak assumption that user-chosen regression procedures estimate conditional means at a sufficiently fast rate that is slow enough to accommodate nonparametric settings. By further assuming stability of the regression procedures and weak dependence in the time series, we can utilise the entire dataset to estimate the conditional means without splitting the time series into subsets.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-18 in stat.ME).
Categorie arXiv: Methodology (stat.ME) ; Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2609.20772 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:03:07.203Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).