{
  "id": "1505.02077",
  "version": "v1",
  "published": "2015-05-08T16:02:06.000Z",
  "updated": "2015-05-08T16:02:06.000Z",
  "title": "Estimating the extremal index through local dependence",
  "authors": [
    "Helena Ferreira",
    "Marta Ferreira"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition D$^{(k)}$($u_n$). We compare a process satisfying one of this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the D$^{(2)}$($u_n$) condition. We also analyze local dependence within moving maxima processes and derive a necessary and sufficient condition for D$^{(k)}$($u_n$). In order to evaluate the performance of the proposed estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a simulation study and compare with existing methods. An application to a financial time series is also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-08T16:02:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "62G32"
    ],
    "keywords": [
      "extremal index",
      "local dependence condition",
      "increasingly weaker local mixing conditions",
      "analyze local dependence",
      "financial time series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}