{
  "id": "1509.05149",
  "version": "v1",
  "published": "2015-09-17T07:26:00.000Z",
  "updated": "2015-09-17T07:26:00.000Z",
  "title": "Iterated scaling limits for aggregation of randomized INAR(1) processes with idiosyncratic Poisson innovations",
  "authors": [
    "Matyas Barczy",
    "Fanni Nedényi",
    "Gyula Pap"
  ],
  "comment": "48 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\\alpha \\in (0, 1)$ and with idiosyncratic Poisson innovations. Assuming that $\\alpha$ has a density function of the form $\\psi(x) (1 - x)^\\beta$, $x \\in (0, 1)$, with $\\lim_{x\\uparrow 1} \\psi(x) = \\psi_1 \\in (0, \\infty)$, different limits of appropriately centered and scaled aggregated partial sums are shown to exist for $\\beta \\in (-1, 0)$, $\\beta = 0$, $\\beta \\in (0, 1)$ or $\\beta \\in (1, \\infty)$, when taking first the limit as $N \\to \\infty$ and then the time scale $n \\to \\infty$, or vice versa. The paper extends some of the results in Pilipauskait\\.e and Surgailis (2014) from the case of random-coefficient AR(1) processes to the case of certain randomized INAR(1) processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-17T07:26:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60J80",
      "60G52",
      "60G15",
      "60G22"
    ],
    "keywords": [
      "idiosyncratic poisson innovations",
      "iterated scaling limits",
      "randomized inar",
      "aggregation",
      "joint temporal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905149B"
    }
  }
}