{
  "annotation_id": "de928bf6-0b23-460e-aa7a-cc4dae2263bb",
  "date_created": "2026-03-02T18:01:11.218000Z",
  "date_modified": "2026-03-02T18:01:11.218000Z",
  "file_hash": "611d2cf7b889f177fb7e439f6add2a9d54644c533d7c70f74a7b3c5df3a968e2",
  "private": false,
  "record": {
    "abstract": "In this paper we investigate the dependence structure for PARMA models (i.e.\nARMA models with periodic coefficients) with symmetric alpha-stable\ninnovations. In this case the covariance function is not defined and therefore\nother measures of dependence have to be used. After obtaining the form of the\nbounded solution of the PARMA system with symmetric alpha-stable innovations,\nwe study the codifference and the covariation -- the most popular measures of\ndependence defined for symmetric stable time series. We show that both\nconsidered measures are periodic. Moreover we determine the cases when the\ncodifference and the covariation are asymptotically proportional with the\ncoefficient of proportionality equal to alpha.",
    "arxiv_id": "physics/0608137",
    "authors": [
      "Joanna Nowicka-Zagrajek",
      "Agnieszka Wylomanska"
    ],
    "categories": [
      "physics.data-an"
    ],
    "title": "The dependence structure for PARMA models with alpha-stable innovations",
    "url": "https://arxiv.org/abs/physics/0608137"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "14350f5d-0f16-4b76-8574-03dd2f20c2c2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}