{
  "id": "math/0503681",
  "version": "v1",
  "published": "2005-03-29T12:53:09.000Z",
  "updated": "2005-03-29T12:53:09.000Z",
  "title": "Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime",
  "authors": [
    "Randal Douc",
    "Eric Moulines",
    "Tobias Ryden"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Statistics 2004, Vol. 32, No. 5, 2254-2304",
  "doi": "10.1214/009053604000000021",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-29T12:53:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62M09",
      "62F12"
    ],
    "keywords": [
      "maximum likelihood estimator",
      "asymptotic properties",
      "markov regime",
      "autoregressive models",
      "hidden markov chain conditional"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Institute of Mathematical Statistics",
      "journal": "Ann. Stat."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3681D"
    }
  }
}