{
  "id": "2001.07127",
  "version": "v1",
  "published": "2020-01-20T14:48:48.000Z",
  "updated": "2020-01-20T14:48:48.000Z",
  "title": "On simultaneous limits for aggregation of stationary randomized INAR(1) processes with Poisson innovations",
  "authors": [
    "Matyas Barczy",
    "Fanni K. Nedényi",
    "Gyula Pap"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate 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 $\\beta\\in(-1,\\infty)$ and $\\lim_{x\\uparrow 1} \\psi(x) = \\psi_1 \\in (0,\\infty)$, different limits of appropriately centered and scaled aggregated partial sums are shown to exist for $\\beta\\in(-1,0]$ in the so-called simultaneous case, i.e., when both $N$ and $n$ increase to infinity at a given rate. The case $\\beta\\in(0,\\infty)$ remains open. We also give a new explicit formula for the joint characteristic functions of finite dimensional distributions of the appropriately centered aggregated process in question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-20T14:48:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60J80",
      "60G52",
      "60G15",
      "60E10"
    ],
    "keywords": [
      "stationary randomized inar",
      "simultaneous limits",
      "aggregation",
      "finite dimensional distributions",
      "joint characteristic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}