{
  "id": "1503.00741",
  "version": "v1",
  "published": "2015-03-02T21:05:19.000Z",
  "updated": "2015-03-02T21:05:19.000Z",
  "title": "On the asymptotic normality of kernel estimators of the long run covariance of functional time series",
  "authors": [
    "István Berkes",
    "Lajos Horváth",
    "Gregory Rice"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We consider the asymptotic normality in $L^2$ of kernel estimators of the long run covariance kernel of stationary functional time series. Our results are established assuming a weakly dependent Bernoulli shift structure for the underlying observations, which contains most stationary functional time series models, under mild conditions. As a corollary, we obtain joint asymptotics for functional principal components computed from empirical long run covariance operators, showing that they have the favorable property of being asymptotically independent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-02T21:05:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic normality",
      "kernel estimators",
      "functional time series models",
      "stationary functional time series",
      "dependent bernoulli shift structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}