{
  "annotation_id": "ba38371b-f067-4c21-a710-f0a3033df780",
  "date_created": "2026-03-02T18:01:24.774000Z",
  "date_modified": "2026-03-02T18:01:24.774000Z",
  "file_hash": "b5d81d74c400a1655024b6b0faec1d7522e6e6da64ad92f2168c3961e3091c04",
  "private": false,
  "record": {
    "abstract": "The schemes for the generation of surrogate data in order to test the null\nhypothesis of linear stochastic process undergoing nonlinear static transform\nare investigated as to their consistency in representing the null hypothesis.\nIn particular, we pinpoint some important caveats of the prominent algorithm of\namplitude adjusted Fourier transform surrogates (AAFT) and compare it to the\niterated AAFT (IAAFT), which is more consistent in representing the null\nhypothesis. It turns out that in many applications with real data the\ninferences of nonlinearity after marginal rejection of the null hypothesis were\npremature and have to be re-investigated taken into account the inaccuracies in\nthe AAFT algorithm, mainly concerning the mismatching of the linear\ncorrelations. In order to deal with such inaccuracies we propose the use of\nlinear together with nonlinear polynomials as discriminating statistics. The\napplication of this setup to some well-known real data sets cautions against\nthe use of the AAFT algorithm.",
    "arxiv_id": "physics/9905021",
    "authors": [
      "D. Kugiumtzis"
    ],
    "categories": [
      "physics.data-an",
      "physics.comp-ph"
    ],
    "doi": "10.1103/PhysRevE.60.2808",
    "title": "Test your surrogate data before you test for nonlinearity",
    "url": "https://arxiv.org/abs/physics/9905021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "935665ca-ec0a-4565-9cea-c063488d7bcf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}