{
  "id": "0806.4263",
  "version": "v1",
  "published": "2008-06-26T08:47:30.000Z",
  "updated": "2008-06-26T08:47:30.000Z",
  "title": "The notion of $ψ$-weak dependence and its applications to bootstrapping time series",
  "authors": [
    "Paul Doukhan",
    "Michael H. Neumann"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/06-PS086 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Probability Surveys 2008, Vol. 5, 146-168",
  "doi": "10.1214/06-PS086",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from a contraction property of the process. Furthermore, we provide an overview of classes of processes possessing the property of weak dependence and describe important probabilistic results under such an assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-26T08:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "62E99"
    ],
    "keywords": [
      "weak dependence",
      "bootstrapping time series",
      "applications",
      "example processes driven",
      "time series bootstrap"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4263D"
    }
  }
}