{
  "method": "EMD",
  "slug": "emd",
  "title": "EMD: estimate envelopes, subtract their mean, and sift",
  "summary": "EMD adapts its oscillatory modes to the extrema of the current signal. DeTime then groups upstream modes into its trend/season/residual result.",
  "steps": [
    {
      "title": "Locate extrema",
      "text": "Local maxima and minima anchor the envelope construction."
    },
    {
      "title": "Build envelopes",
      "text": "PyEMD interpolates upper and lower envelopes with its boundary treatment."
    },
    {
      "title": "Sift",
      "text": "Subtract their pointwise mean, recompute extrema, and apply the stopping criteria."
    },
    {
      "title": "Remove the IMF",
      "text": "Subtract the accepted mode from the signal and continue on the remainder."
    }
  ],
  "parameters": [
    {
      "name": "n_imfs",
      "effect": "Limits extracted modes in DeTime's PyEMD call; a final residue can also be returned."
    },
    {
      "name": "primary_period / explicit IMF groups",
      "effect": "Controls DeTime's subsequent grouping; it does not determine the sifting envelopes."
    },
    {
      "name": "PyEMD stopping criteria",
      "effect": "This trace uses the upstream defaults; DeTime's wrapper exposes a narrower parameter surface."
    }
  ],
  "cautions": [
    "EMD modes are not uniquely identified physical sources; the first mode is not automatically the desired season.",
    "Spline boundary choices and added observations can change previously estimated components.",
    "The animation records the first IMF; it does not imply the algorithm stops after one mode."
  ],
  "references": [
    {
      "title": "PyEMD EMD algorithm and envelope API",
      "url": "https://pyemd.readthedocs.io/en/latest/emd.html"
    },
    {
      "title": "Huang et al. (1998)",
      "url": "https://doi.org/10.1098/rspa.1998.0193"
    }
  ],
  "trace_kind": "upstream execution trace",
  "trace_note": "Envelope calls recorded from EMD-signal 1.10.0 with default sifting settings and max_imf=1. All curves are computed; no intermediate curve is interpolated between final results.",
  "input_note": "Deterministic synthetic teaching signal; not a benchmark.",
  "example_config": {
    "method": "EMD",
    "params": {
      "n_imfs": 3,
      "primary_period": 24
    }
  },
  "checks": {
    "recorded_sifts": 11,
    "imf_plus_remainder_max_abs_error": 2.220446049250313e-16,
    "sequential_sift_update_error": 0.0,
    "final_sift_matches_first_imf": 0.0,
    "finite_sifts": true
  },
  "source_files": [
    "src/detime/methods/emd.py"
  ],
  "frames": 32,
  "duration_ms": 12050,
  "poster_frame": 15,
  "width": 1280,
  "height": 820,
  "artifacts": {
    "gif": {
      "file": "emd.gif",
      "bytes": 450248,
      "sha256": "67b3c109bce56b68f572ae368b80c9c7ec42078839fd1729c9efb242eeaf2e04"
    },
    "poster": {
      "file": "emd.png",
      "bytes": 186211,
      "sha256": "5da1acc1afe87523606fb8f2d74e738be8310ae12ba025928ef254e870186ff8"
    },
    "data": {
      "file": "emd.npz",
      "bytes": 49095,
      "sha256": "8cf09db8ba2515d039ed48306aebeebc8a4ae62361d81c73f06c97f409c50a17"
    }
  },
  "source_arrays": {
    "time": [
      192
    ],
    "input": [
      192
    ],
    "sift_candidate_upper_lower": [
      11,
      3,
      192
    ],
    "first_imf": [
      192
    ],
    "remainder": [
      192
    ],
    "maxima": [
      23
    ],
    "minima": [
      23
    ]
  },
  "render_provenance": {
    "python_version": "3.11.3",
    "dependencies": {
      "numpy": "2.4.6",
      "scipy": "1.17.1",
      "statsmodels": "0.15.0",
      "matplotlib": "3.11.2",
      "Pillow": "13.0.0",
      "PyWavelets": "1.9.0",
      "EMD-signal": "1.10.0",
      "vmdpy": "0.2",
      "PySDKit": "0.5.0"
    },
    "source_hashes": {
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  }
}