{
  "id": "2009.13189",
  "version": "v1",
  "published": "2020-09-28T10:03:30.000Z",
  "updated": "2020-09-28T10:03:30.000Z",
  "title": "SPHARMA approximations for stationary functional time series on the sphere",
  "authors": [
    "Alessia Caponera"
  ],
  "categories": [
    "math.ST",
    "math.PR",
    "stat.TH"
  ],
  "abstract": "In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in [8, 7]; more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-28T10:03:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62M15",
      "62M10",
      "60G15",
      "60F05",
      "62M40",
      "60G60"
    ],
    "keywords": [
      "stationary functional time series",
      "spharma approximations",
      "stationary sphere-cross-time random field",
      "functional autoregressive-moving average processes",
      "functional spectral representation theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}