SPY VaR

Classical and neural models for one-day tail-risk forecasting

Report · Methods · Results · Reproduce · References · Editable figures

A reproducible study of 1%, 5% and 10% conditional return quantiles for SPY. The project combines statistical volatility models, neural quantile regression, and a conservative GARCH-anchored correction, with an additional PatchTST-inspired quantile Transformer trained from scratch.

Figure 1. Research workflow. Numerical panels use the included SPY snapshot. The model and evaluation blocks correspond to executable code.

Study at a glance

Item	Specification
Instrument and period	SPY; 2000-01-04–2018-06-27
Data	4,640 observations; decimal log returns, rv5 and bv
Task	One-trading-day-ahead lower return quantiles
Quantile levels	0.01, 0.05, 0.10
New-run estimation window	1,000 observations; explicit model-specific refit schedules
Evaluation	Common finite target dates; coverage, independence and pinball loss
Evidence	Preserved historical forecasts and separately reported new three-seed Transformer runs

The research question is whether structured volatility information and controlled nonlinear corrections can improve tail-risk calibration. No single model is assumed to dominate. Coverage calibration and forecast loss answer different questions, and a non-rejected backtest is not proof that a model is correct.

Models and scientific basis

Model	Actual implementation	Basis / status
Ordinary HS	Equal-weight empirical quantile	Transparent statistical baseline
Time-weighted HS	Exponential age weights, decay 0.98	Inverse weighted empirical CDF
KDE weighted HS	Weighted Gaussian KDE, Scott bandwidth	Smoothed distributional baseline
GARCH-t	Constant mean, GARCH(1,1), standardized Student-t innovations	Bollerslev, 1986
GJR-GARCH-t	Asymmetric conditional variance, Student-t innovations	Glosten et al., 1993
MLP quantile regression	Lag-window MLP, 64→32→3, pinball loss	Project baseline; quantile objective
C2 anchored correction	18→64→32→3; nonnegative softplus correction subtracted from GARCH quantiles	Project-specific exploratory model
Patch-based quantile Transformer	64 returns → 7 patches → 2 encoder layers → 3 quantiles	Project adaptation of PatchTST, ICLR 2023

Canonical implementations are under src/spy_var/models. Methods states the information available at each forecast date and distinguishes project changes from the cited original methods.

Conservative GARCH-anchored correction

Figure 2. Implemented C2 architecture. Circle counts are schematic; the labeled layer widths and feature dimensions are exact. The historical C2 regularization setting was selected after inspecting test-period results, so its calibration evidence remains exploratory.

Patch-based quantile Transformer

Figure 3. Implemented neural extension. This is a small one-day quantile adaptation inspired by PatchTST, not the original authors' long-horizon point-forecasting model. It replaces MSE with pinball loss and uses RevIN-style per-window normalization without learnable affine parameters. The exact 18,531-parameter configuration and all implementation differences are documented.

Empirical results

Archived common-date comparison

All six rows below use the same 2,640 target dates, 2008-01-03–2018-06-27, and the 1% quantile. The table is recomputed from the preserved predictions; it is not a new training run. Losses are in decimal-return units.

Model	Violations / 2,640	Rate	Kupiec p	Independence p	Pinball loss
Time-weighted HS	41	1.55%	0.00825	0.0275	0.000410
KDE weighted HS	36	1.36%	0.0752	0.0127	0.000400
GARCH-t	41	1.55%	0.00825	0.163	0.000358
GJR-GARCH-t	38	1.44%	0.0333	0.577	0.000334
Lag-window MLP	14	0.53%	0.00772	0.699	0.001523
C2 correction	25	0.95%	0.782	0.0217	0.000350

C2 has near-nominal unconditional coverage in this sample, while its 1% independence test rejects at the unadjusted 5% level. GJR-GARCH has lower pinball loss in this comparison. These observations support a calibration/loss trade-off, rather than a claim of uniform neural-model superiority.

Figure 4. Actual archived forecasts. The top row uses all three quantiles; the lower panel includes all observed returns and C2 1% violations on the aligned dates. Complete final table.

New Transformer runs

The fixed configuration was run from scratch with seeds 42, 43 and 44 on the complete snapshot. Each seed yields 3,640 forecasts. These runs use a longer evaluation period than the archived C2-aligned table and are therefore reported separately.

Nominal quantile	Observed rate, mean ± SD	Pinball loss, mean ± SD	Dates per seed
1%	2.26% ± 0.10 pp	0.000389 ± 0.000004	3640
5%	5.60% ± 0.22 pp	0.001243 ± 0.000011	3640
10%	10.13% ± 0.35 pp	0.001997 ± 0.000006	3640

SD is the sample standard deviation across optimization seeds; pp means percentage points. It is not a confidence interval and does not increase the number of independent market observations. The 1% forecasts remain under-calibrated: actual violations average about 2.26%, and the per-seed unconditional-coverage tests reject. This extension is an evaluated comparison model, not an asserted improvement.

Per-seed metrics · Final summary · Experiment fingerprints and checks

Reproduce

Use Python 3.12. From the repository root:

python -m venv .venv
# Windows PowerShell:
.\.venv\Scripts\Activate.ps1
# macOS / Linux: source .venv/bin/activate
python -m pip install -r requirements-lock.txt

Evaluate archived predictions, with no model fitting:

python scripts/reproduce.py evaluate --include-c2 --output ../spy-var-runs/cached-c2

Check all model families on a small chronological sample:

python scripts/reproduce.py train --config configs/smoke.json --max-observations 160 --output ../spy-var-runs/smoke

Reproduce the new full-snapshot neural experiment:

python scripts/reproduce.py train --config configs/modern_quantile.json --seeds 42 43 44 --output ../spy-var-runs/patch-seeds

The baseline and full C2 configurations remain available under configs. Run directories record expanded settings, data/code fingerprints, predictions, optimizer diagnostics and dated training losses. Existing nonempty output directories are rejected. Detailed runs and figure build files stay outside the checkout; only compact final evidence is retained.

Complete reproduction guide · Executed validation

Repository structure

SPY_VaR/
├── configs/                 # Explicit baseline, C2, Transformer and smoke settings
├── src/spy_var/
│   ├── models/              # Statistical, MLP, anchored and patch models
│   ├── data.py              # Chronological snapshot validation
│   ├── artifacts.py         # One registry for historical prediction files
│   ├── backtesting.py       # Common-sample statistical evaluation
│   └── pipeline.py          # Experiments, provenance and seed summaries
├── scripts/                 # Reproduction and final figure/result publication
├── tests/                   # Timing, statistics, model and evidence checks
├── docs/
│   ├── figures/             # Four final PNGs and their editable PPTX
│   ├── results/             # Compact, verified final metric tables
│   ├── METHODS.md
│   ├── EXPERIMENTS.md
│   └── REFERENCES.md
├── code/                    # Preserved report chapters, data and historical outputs
└── Final_Report_Single.pdf

The original chapter materials remain available for the report. New experiments use a single canonical implementation and data snapshot.

Scope and limitations

This is a retrospective, single-asset historical study. Extreme-tail events are sparse, C2's inherited regularization was selected after test inspection, and the new Transformer does not achieve nominal 1% coverage. An independent future sample is needed before making a confirmatory forecasting claim. The work does not establish general superiority of neural methods or a trading strategy.

The diagrams are original, code-matched compositions. Their numerical panels use real repository data. They were built with EditableImage2PPTSkill, refined as native PowerPoint objects, and exported from the saved PPTX. Figure sources and README design references include a dated, conservative verification of the high-star reference selection.

Citation and license

Use CITATION.cff and include the commit used in your experiment. Original methods are credited in References; the project does not declare a paper DOI.

Code: MIT. Homepage: cloudcollection.github.io.