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Statsmodels MSTL wrapper

Statsmodels MSTL wrapper

Property Value
Method MSTL
Input mode univariate
Trend shape (96,)
Notebook execution ran
Reconstruction RMSE 0.00000000

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: stable. Implementation: wrapper.

MSTL repeatedly estimates one seasonal period while removing the current estimates of the others, then returns a trend and remainder.

MSTL: Specify the seasonal periods; Estimate seasonal terms; Add back and refine each term; Aggregate the common output

Deterministic synthetic teaching signal; not a benchmark.

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

Follow the four steps

1. Specify the seasonal periods

Supply the periods and their seasonal smoothing windows. This synthetic signal contains periods 12 and 36, and both are specified explicitly. The FFT panel describes the input; it is not an automatic period-selection stage in the wrapper.

2. Estimate seasonal terms

Initialize seasonal arrays at zero. For each period in the upstream processing order, fit STL to the currently adjusted series and subtract the estimated seasonal term before processing the next period.

3. Add back and refine each term

On each later pass, add back the previous estimate for the period being updated, refit that seasonal term, and subtract its replacement. This preserves the other current seasonal estimates while refining one term at a time.

4. Aggregate the common output

Use the trend from the last STL fit and subtract it from the deseasonalized series to obtain residual. DeTime sums separate upstream seasonal columns into result.season. This animation uses lmbda=None; transformed fits require the wrapper's documented original-scale allocation.

Parameters that change the result

Parameter Effect on the computation
periods One or more integer cycle lengths. Upstream MSTL sorts them and filters periods that are too long for the record.
windows Odd seasonal-smoothing spans paired with the periods; this example uses 11 and 15.
iterate Number of passes over the seasonal terms; this example uses two.
lmbda Optional Box-Cox transform. None keeps the additive trace in the original scale; transformed components cannot be inverted independently and then simply added.
stl_kwargs Options forwarded to each STL fit, including its robustness setting.

What this animation computes

The alternating STL loop follows the installed statsmodels MSTL.fit procedure with an explicit two-period, no-transform setup. Its separate seasonal estimates, final trend, and public DeTime output are checked numerically.

Interpretation

  • Choose periods with enough observed repetitions. The example is illustrative and does not identify periods from data.
  • Closely related periods and smoothing choices can change how variation is allocated between seasonal terms.
  • DeTime's common season field is the sum of upstream seasonal columns; individual periods in this animation are instrumented from the upstream procedure.
  • For Box-Cox fits, DeTime uses inverse(T) for trend and inverse(T+S)-inverse(T) for combined season, with the remaining difference in residual. This no-transform trace does not animate that nonlinear allocation.

Try the method

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

{
  "method": "MSTL",
  "backend": "python",
  "params": {
    "periods": [
      12,
      36
    ],
    "windows": [
      11,
      15
    ],
    "iterate": 2,
    "lmbda": null
  }
}

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

Sources and reproduction

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

Code

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

Output

MSTL: Statsmodels MSTL wrapped into the DeTime workflow surface.
status: ran
input mode: univariate
trend shape: (96,)
backend: python
reconstruction RMSE: 0.00000000

Decomposition Plot

MSTL decomposition