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Notebook example metric: root mean square of input - (trend + season + residual) over all samples and channels. This checks additive bookkeeping; it is not a forecast error or a component-recovery score. The separate teaching input and intermediate arrays for the animation are linked below.

How it works

Method maturity: maintained. Implementation: native-backed.

STDR uses a phase-wise average of normalized cycle shapes, then restores each cycle's dispersion and keeps a remainder.

Deterministic synthetic teaching signal; not a benchmark.

Open GIF · Static PNG · Source arrays (NPZ) · Trace metadata

Follow the four steps

1. Partition and center cycles

Split at the configured period, compute each block's arithmetic mean, and subtract it. DeTime assigns that mean to every sample of the block, producing a piecewise-constant trend. A final partial block uses the samples that exist.

2. Separate dispersion and shape

Compute the Euclidean norm of each centered block as its dispersion. Divide by that norm to obtain a unit-length seasonal shape. A block whose norm is below eps receives zero dispersion and a zero shape.

3. Average shapes across cycles

Average normalized shape entries at the same phase across cycles. For a partial cycle, increment counts only for available phases. Multiply this shared average by each cycle's own dispersion; the average shape is not normalized again.

4. Compute the common result

Return trend, the scaled seasonal term, and residual = observed - trend - season, plus dispersion and seasonal-shape arrays. Deviations from the common cycle shape remain in the residual. In the cited formulation, R denotes a remainder; the code does not perform robust reweighting.

Parameters that change the result

What this animation computes

Every stage follows compute_std_components and the corresponding native kernel: block means, Euclidean norms, phase counts, and scaling. Both direct-source and public Python outputs are compared. The final short block is intentional.

Interpretation

• DeTime's STD/STDR use block means and L2 norms. Dispersion is not the sample standard deviation.
• STDR uses ordinary phase-wise means of normalized shapes. No robust loss, trimming, or outlier weights are used in this implementation.
• A partial cycle has its own mean and norm and contributes only available phases; its scale is not directly comparable to a full cycle without accounting for length.
• STD retains within-cycle irregular variation in its shape. STDR assigns deviations from a shared shape to the remainder.
• The supplied period and the starting phase define block boundaries; shifting the start changes the decomposition.

Try the method

Use this configuration with DecompositionConfig and decompose. The animation generator supplies the teaching input and records intermediate arrays.

{
  "method": "STDR",
  "backend": "python",
  "params": {
    "period": 24
  }
}

See the configuration reference for the full interface and optional dependencies.

Sources and reproduction

• Dudek (2022), STD: A Seasonal-Trend-Dispersion Decomposition of Time Series
• DeTime implementation: src/detime/methods/std.py
• DeTime implementation: native/src/std.cpp

Regenerate this animation with python scripts/generate_method_animations.py --methods STDR. The reproduction guide explains the environment, numerical checks, coverage manifest, and how to inspect the stored arrays.

Code

case = CASES["STDR"]
run_gallery_case("STDR")

Output

STDR: Seasonal-trend-dispersion decomposition with an averaged cycle shape and a remainder.
status: ran
input mode: channelwise
trend shape: (96,)
backend: native
reconstruction RMSE: 0.00000000

Decomposition Plot