Reproduction: Beyond Model Ranking

1SCP complexity ★ REPRODUCED

Welch spectral estimates produce a linear lower bound per forecast window. Median wall time tracks N log N over N = 256–32,768.

R-squared 0.9990 for runtime versus N log N, reaching 0.777 ms at the largest tested length.

2Boundedness & consistency

For centered jointly Gaussian data, P_xy = 1 − MSE_lb/Var(y) converges when the effective number of Welch segments grows.

At N = 65,536, absolute error is 0.000361. A mean-shift example gives raw P = −15.44, exposing the missing condition.

QUALIFIED: [0,1] requires the paper's centering assumptions.

3Does lower bound predict error?

We tested four public ETT datasets with five transparent forecasters. This is a scope-controlled proxy, not the paper's trained iTransformer/TimeMixer/PatchTST matrix.

Six of 20 pairs reach R ≥ 0.8; median R across pairs is 0.653.

Dataset	Best R	Forecaster
ETTh1	0.878	Mean
ETTh2	0.967	Mean
ETTm1	0.973	Mean
ETTm2	0.991	Mean

PARTIAL: no released checkpoints and no funded GPU Job.

!Compute boundary

The Hugging Face Jobs canary was rejected before scheduling with HTTP 402 for insufficient prepaid credit; no cloud compute ran.

Local CPU: AMD Ryzen 7 7700.
Public data: ETTh1, ETTh2, ETTm1, ETTm2.
All predictions and raw tables are bundled.

Scope	This run
Models	5 lightweight
Pairs	20
Cloud cost	$0

4Predictability drifts ★ REPRODUCED

A full stride-1 ETTh1 test sweep measures 2,545 windows per channel with 336-step histories and horizons.

Channel 1 spans P = 0.100–0.659, a 0.558 swing. Mean predictability differs by 0.309 across seven channels.

2,545

windows per
channel

7

ETTh1
variables

0.558

temporal
swing

Channel	Mean P	Range
0	0.497	0.647
1	0.404	0.558
2	0.513	0.693
3	0.418	0.545
4	0.319	0.551
5	0.204	0.383
6	0.218	0.648

DWhy drift matters

A dataset average mixes easy and hard windows. SCP exposes difficulty changes and separates model quality from target-process changes.

Drift check	Observed
Channel 1 swing	0.558
Smallest channel swing	0.383
Mean-P spread	0.309

Report where performance occurs—not merely global rank.

5Frequency-resolved LUR ★ REPRODUCED

LUR compares forecast improvement against the exploitable linear signal in each frequency band.

Linear trend under-uses signal (median 0.223); the copy control saturates at 1.000; an oracle control exceeds linear at 2.603.

Diagnostic	Median LUR	Regime
Trend	0.223	Under-use
Copy control	1.000	Saturation
Ridge	1.275	Beyond-linear
Oracle	2.603	Beyond-linear

Ten frequency bands locate the scales each forecast exploits.

RReproduction contract

Seven unit tests cover spectral and window logic.
Every plot is regenerated from public data.
Raw tables, predictions, code, and environment lock are public.
Limits remain explicit rather than becoming confirmations.

Bundle item	Format
Raw metrics	CSV / JSON
Predictions	NPZ
Figures	PNG
Environment	uv.lock
Tests	pytest