{
  "abstract": "We study estimation and inference for a semiparametric class of time series models that specify only the conditional expectation, which is a known link function applied to a linear combination of past observations and covariates. The class covers count, binary, bounded and conditionally heteroskedastic responses within a single formulation, and the parameter is estimated by a quasi-likelihood estimating equation based on the first conditional moment. Under stationarity and a weak-dependence condition expressed through the functional dependence measure, we establish two results. First, using a Fuk--Nagaev inequality for weakly dependent sequences, we show that the estimator is localized in a shrinking neighbourhood of the true value with probability $1-o(n^{-1/2})$. Second, combining a Berry--Esseen bound for weakly dependent sequences with a Gaussian anti-concentration argument to control the remainder of the linear expansion, we obtain a Berry--Esseen bound for linear projections of the estimator, uniform over projection directions. From the projected bound we derive studentized confidence intervals with explicit coverage error and a conservative Bonferroni test for linear hypotheses on the parameters. For real data analysis, we extend the Beta autoregression for double-bounded data to an arbitrary link given by the inverse of a distribution function, and apply it to ten pairwise realized correlations of large-cap technology-stock returns, using Nasdaq and Dow~Jones index returns as covariates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04613",
  "author_total": 2,
  "authors": [
    {
      "name": "Zinsou Max Debaly"
    },
    {
      "name": "Arsene Brice Zotsa-Ngoufack"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nmvwyda7afbt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04613",
  "fulltext_url": null,
  "id": "9nmvwyda7afbt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04613",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7211865540",
  "pdf_url": "https://arxiv.org/pdf/2609.04613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nmvwyda7afbt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Uniform Gaussian Approximation for The Quasi-Likelihood Estimator for a Weakly Dependent Nonlinear Time Series Models",
  "title_text": "Uniform Gaussian Approximation for The Quasi-Likelihood Estimator for a Weakly Dependent Nonlinear Time Series Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:25Z",
  "url": "https://research.draconitic.com/paper/9nmvwyda7afbt",
  "venue": "arXiv",
  "versions": []
}