{
  "annotation_id": "43733fd9-d1b9-47d2-98c0-949d4080a49e",
  "date_created": "2026-03-02T18:00:35.184000Z",
  "date_modified": "2026-03-02T18:00:35.184000Z",
  "file_hash": "74afe97ba531758be3f8b453ee8491f24f2c711625efca0f4ea5147618b84ccf",
  "private": false,
  "record": {
    "abstract": "Detrended fluctuation analysis (DFA) is a scaling analysis method used to\nestimate long-range power-law correlation exponents in noisy signals. Many\nnoisy signals in real systems display trends, so that the scaling results\nobtained from the DFA method become difficult to analyze. We systematically\nstudy the effects of three types of trends -- linear, periodic, and power-law\ntrends, and offer examples where these trends are likely to occur in real data.\nWe compare the difference between the scaling results for artificially\ngenerated correlated noise and correlated noise with a trend, and study how\ntrends lead to the appearance of crossovers in the scaling behavior. We find\nthat crossovers result from the competition between the scaling of the noise\nand the ``apparent\u0027\u0027 scaling of the trend. We study how the characteristics of\nthese crossovers depend on (i) the slope of the linear trend; (ii) the\namplitude and period of the periodic trend; (iii) the amplitude and power of\nthe power-law trend and (iv) the length as well as the correlation properties\nof the noise. Surprisingly, we find that the crossovers in the scaling of noisy\nsignals with trends also follow scaling laws -- i.e. long-range power-law\ndependence of the position of the crossover on the parameters of the trends. We\nshow that the DFA result of noise with a trend can be exactly determined by the\nsuperposition of the separate results of the DFA on the noise and on the trend,\nassuming that the noise and the trend are not correlated. If this superposition\nrule is not followed, this is an indication that the noise and the superimposed\ntrend are not independent, so that removing the trend could lead to changes in\nthe correlation properties of the noise.",
    "arxiv_id": "physics/0103018",
    "authors": [
      "Kun Hu",
      "Plamen Ch. Ivanov",
      "Zhi Chen",
      "Pedro Carpena",
      "H. Eugene Stanley"
    ],
    "categories": [
      "physics.data-an",
      "cond-mat.stat-mech",
      "physics.bio-ph"
    ],
    "doi": "10.1103/PhysRevE.64.011114",
    "journal_ref": "Physical Review E, vol. 64, 011114, 2001",
    "title": "Effect of Trends on Detrended Fluctuation Analysis",
    "url": "https://arxiv.org/abs/physics/0103018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cc103c4-b4a1-4895-92f1-53be7dd4a257",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}