tamzidullah/quantura-ensemble-study-2026

Chronological Optimization of a Seven-Model Time-Series Quantile Ensemble

Revised October 18, 2026. This is the corrected seven-model study. The original six-model paper omitted TimesFM and did not fulfill the seven-member scope. Original paper/source are archived under archive/six-model-2026-10-17/; the original implementation and four-target data at repository root remain unchanged for reproducibility. Use seven-model-v2/ for the revised study.

Downloads

• Corrected seven-model paper (PDF)
• Complete code, data, all ledgers and tests (ZIP)
• Author submission source (TAR.GZ)
• Protocol and results guide
• Independent calculation checks
• Frozen configurations and weights
• Raw forecast ledger archive

No arXiv ID is claimed. This is repository hosting of a technical preprint, not a peer-reviewed publication or a Hugging Face Paper Page.

Seven participants, two Toto sizes

Prophet; Toto 2.0; IBM Granite; Amazon Chronos-2; Google TimesFM 3.0; Mistral Timestral-209M; The Forecasting Company T0 Gamma. The alternative replaces Toto 4M with the largest official 2.5B checkpoint, keeping seven members. There is no claimed official 4B Toto checkpoint.

Results and limitations

Scores below are scaled seven-quantile pinball loss (lower is better), averaged within each source group and then across the three additional source groups.

Configuration	Loss
Old seven-model LP weighting	0.235472
Legacy inference + inner-selected seven-model weights	0.232057
Refined inference + inner weights, Toto 4M	0.233883
Same refined ensemble with Toto 2.5B	0.234465
Joint calibration selector	0.233552
Granite alone	0.229369

The best tested ensemble cell is 1.45% lower than the old optimizer. Selecting that cell after comparing test scores is descriptive comparison, not another untouched validation. The separately frozen joint calibration selector improves 0.82% and has 79.95% nominal-80% interval coverage under source-group averaging. Granite alone remains stronger. The larger Toto checkpoint and enabling all inference changes do not improve the additional-cohort aggregate.

The study contains 1,584 actual model-origin evaluations across 11 targets. Seven additional targets produce 992 final test scalar outcomes but only three source groups; correlated weather stations are not independent confirmations. The original four targets (192 final test outcomes) remain retrospective. Historical foundation-model pretraining overlap is unknown. No statistical significance, globally optimal weights, production SLA or trading returns are claimed. Seven central participants become five eligible P01/P99 participants; Toto/TimesFM tails are never fabricated.

Reproduction and provenance

The complete ZIP is self-contained. In the browsable seven-model-v2/ tree, extract forecast_ledger.zip in its containing results folder before evaluation. The original protocol and separately committed pre-scoring joint-selection addendum are released with data source URLs, transformations, immutable revisions, run/failure provenance and per-file SHA-256 checksums. Publication calculations are independently checked to 1e-12. The research GitHub Actions were disabled after completion; the production repository stayed private and paused.

Licensing and disclosure

Paper/figures: CC BY 4.0. Code: MIT. UCI-derived Bike Sharing data (Fanaee-T, 2013, DOI 10.24432/C5W894) and Beijing Multi-Site Air Quality data (Chen, 2017, DOI 10.24432/C5RK5G): CC BY 4.0, with selected targets/windows described in the manifest. Statsmodels example datasets retain public-domain notices. Model weights are not included and retain their separate licenses. TimesFM 3.0 is used in non-commercial, non-production research test mode; this does not authorize commercial self-hosted deployment. Timestral weights have a modified MIT license.

Tamzid Ullah develops Quantura and has a commercial interest in the product. AI assistance supported implementation, analysis and drafting. The author remains responsible for review. No vendor endorsement is implied. No customer data, credentials or private application history are published.