{
  "abstract": "Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a reproducing kernel Hilbert space (RKHS)-based test for nonlinear Granger non-causality in conditional mean for nonlinear autoregressive processes. The key idea is a conditional-centering decomposition of the target regression function into an own-history component and an orthogonal component capturing the additional predictive contribution of the potential source history. Non-causality is characterized by the vanishing of the latter component. The own-history component is estimated by kernel ridge regression, and the residuals are embedded in a second RKHS using a conditionally centered kernel. This yields an RKHS-valued residual moment whose squared norm forms the test statistic. We establish a weighted chi-square null limit and consistency against fixed alternatives for the population-centered statistic. An empirically centered version is shown to retain the null limit and enables spectral calibration of critical values and $p$-values without resampling. Simulation studies demonstrate accurate size control and power against nonlinear alternatives, and real-data applications illustrate the usefulness of the method for detecting nonlinear predictive relationships in time series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22007",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuhan Tian"
    },
    {
      "name": "Adam Waterbury"
    },
    {
      "name": "Marie-Christine Düker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e58acayars95a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22007",
  "fulltext_url": null,
  "id": "e58acayars95a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22007",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7213908476",
  "pdf_url": "https://arxiv.org/pdf/2609.22007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e58acayars95a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:12Z",
      "native_id": "2609.22007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22007"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "RKHS-Based Inference for Nonlinear Granger Causality via Conditional Centering",
  "title_text": "RKHS-Based Inference for Nonlinear Granger Causality via Conditional Centering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:12Z",
  "url": "https://research.draconitic.com/paper/e58acayars95a",
  "venue": "arXiv",
  "versions": []
}