{
  "abstract": "Expected shortfall is defined as the truncated mean of a random variable that falls below a specified quantile level and is widely recognized as an important risk measure. Motivated by the empirical observation of clustering patterns in financial risks, we consider a joint autoregressive model for both conditional quantile and expected shortfall. Existing estimation methods for such models typically rely on minimizing a nonlinear and nonconvex joint loss function, which is challenging to solve. We introduce a two-step regression framework to estimate the model parameters with theoretical guarantees. We further develop a Portmanteau test for model diagnostics and prove its asymptotic validity for Type I error control. Our empirical results on stock market data indicate that the proposed models effectively capture the clustering patterns and leverage effects on the conditional expected shortfall.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25730",
  "author_total": 3,
  "authors": [
    {
      "name": "Peiyao Cai"
    },
    {
      "name": "Kean Ming Tan"
    },
    {
      "name": "Xuming He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/974mka7w1xkz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25730",
  "fulltext_url": null,
  "id": "974mka7w1xkz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25730",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.OT"
    ],
    [
      "openalex",
      "2003|Financial Risk and Volatility Modeling"
    ]
  ],
  "openalex": "W7223062747",
  "pdf_url": "https://arxiv.org/pdf/2610.25730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/974mka7w1xkz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.25730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Estimation and Inference for the Joint Autoregressive Quantile-Expected Shortfall Model",
  "title_text": "Estimation and Inference for the Joint Autoregressive Quantile-Expected Shortfall Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/974mka7w1xkz9",
  "venue": "arXiv",
  "versions": []
}