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WP40 RAID: manuscript v1.0 (30 p., 0 undefined refs), Phase 6–7 ledgers, README headline results

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Simon-Pierre Boucher committed (Nov 2, 2026) parent d628c80 Browse files

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modified README.md +15 −7
@@ -3,7 +3,7 @@
3 3
4 4 **UQO Working Paper No. 40** — *A Metal-Accelerated C++ Framework for Reproducible High-Frequency Financial Econometrics*
5 5
6 −[![Paper](https://img.shields.io/badge/paper-in%20progress-lightgrey?logo=latex&logoColor=white)](paper/)
6 +[![Paper](https://img.shields.io/badge/paper-PDF%20(30%20p.)-b31b1b?logo=latex&logoColor=white)](paper/main.pdf)
7 7 [![C++20](https://img.shields.io/badge/C%2B%2B-20-00599C?logo=cplusplus&logoColor=white)](CMakeLists.txt)
8 8 [![Metal](https://img.shields.io/badge/Metal-4%20(FP32)-000000?logo=apple&logoColor=white)](backends/metal/)
9 9 [![Python](https://img.shields.io/badge/python-3.12%2B%20nanobind-3776AB?logo=python&logoColor=white)](pyproject.toml)
@@ -16,7 +16,7 @@
16 16 > Silicon **without** losing estimator accuracy, inference validity or reproducibility. It is a C++20 library with a FP64
17 17 > CPU reference backend, an optional FP32 Metal backend (Apple GPUs have no FP64), nanobind Python bindings, a CLI, a
18 18 > FinData OS client, and a benchmark protocol that reports break-even points and the cases where the CPU wins.
19 −> Status: Phase 1 (foundation) — see `RESEARCH_STATUS.md`. No performance numbers are claimed yet.
19 +> Status: Phases 0–7 complete (2026-11-02); Phase 8 review in progress — see `RESEARCH_STATUS.md`.
20 20
21 21 ---
22 22
@@ -24,10 +24,10 @@
24 24
25 25 | Item | Value |
26 26 |---|---|
27 −| Version | 0.1.0 (November 2026) — Phases 0–1 |
27 +| Version | 1.0 (November 2026) — manuscript v1.0, library 0.1.0 |
28 28 | SSRN | not yet submitted |
29 29 | Journal | targets: J. Financial Econometrics, J. Financial Data Science, J. Computational Finance |
30 −| Code & data | CPU core + tests build and pass on macOS 27 / Xcode 27.2; synthetic fixtures only in git; real bars via FinData OS (private license) |
30 +| Code & data | 55 test cases pass on macOS 27 / Xcode 27.2 (CPU + Metal); synthetic fixtures only in git; real bars via FinData OS (private license, not redistributed); every table/figure generated from `experiments/results/` |
31 31 | Ledger | `RESEARCH_STATUS.md` · `docs/PROGRESS.md` · `docs/DECISIONS.md` · `docs/risks.md` |
32 32
33 33 ## 🎯 What this paper does
@@ -42,8 +42,15 @@ Gaussian/Student-t QML, block bootstrap) are validated against R `highfrequency`
42 42
43 43 ## 🏆 Headline results
44 44
45 −None yet — benchmarks (E1–E7) run in Phase 6; every number in the paper will point to a record under
46 −`experiments/results/` listed in `experiments/manifests/`.
45 +| Finding | Evidence |
46 +|---|---|
47 +| Metal (FP32 double-float) matches FP64 within 1e−6 on realized measures/regression statistics and 2e−5 on GARCH likelihoods; bitwise reproducible across runs and thread counts | `tests/unit/test_metal_backend.cpp`, `experiments/results/raw/e5_inference.jsonl` |
48 +| Fused realized kernel: Metal wins from ≈ 4×10⁴ elements, 2.0–3.4× vs 18-thread CPU at 4×10⁶–4×10⁷ (kernel level); 1.07–1.41× at the estimator level on 40 M real returns | `bench_primitives_summary.json`, `raw/e1_batched_rv.jsonl` |
49 +| Batched GARCH likelihood grids: 5.1× (888 series × 256 vectors) to 7.9×; single-vector recursions: CPU wins | `raw/e3_garch.jsonl`, `raw/bench_primitives.jsonl` |
50 +| Rolling sums: CPU wins at every size (negative result) | `raw/bench_primitives.jsonl` |
51 +| Parquet→estimates pipeline: 20 M bars/s (RAID CPU) vs 14 M (Polars, DuckDB) vs 0.9 M (pandas); column projection mattered more than any kernel | `raw/e6_pipeline.jsonl`, `raw/e6_baselines.jsonl` |
52 +| 11 Apple Silicon machines (M2→M6): all Metal tests pass; GPU speedup 4.0× (M2) → 1.1× (M5 Max) — largest where the CPU is weakest | `raw/e7/`, `e7_summary.json` |
53 +| Tier A reproduces highfrequency / rugarch / statsmodels / arch to documented tolerances; Monte Carlo coverage 0.90–0.97 | `tests/reference/`, `docs/methods/registry.md` |
47 54
48 55 ## 🗂 Repository layout
49 56
@@ -86,7 +93,8 @@ See `docs/methods/registry.md` (one entry per method: equations, conventions, re
86 93
87 94 ## 🖼 Figures & tables inventory
88 95
89 −To be generated in Phase 6–7 from `experiments/results/`.
96 +Generated by `experiments/scripts/make_paper_assets.py` (hashes in `experiments/manifests/paper_assets.json`):
97 +`paper/tables/tab_{primitives,e1,e2_accuracy,e2_runtime,e3_fits,e4,e5,e6,e7}.tex`, `paper/figures/fig_{primitives_throughput,e1,e7}.pdf`.
90 98
91 99 ## ⚠️ Limitations
92 100
modified RESEARCH_STATUS.md +14 −6
@@ -1,6 +1,6 @@
1 1 # RESEARCH_STATUS.md — RAID (UQO WP 40)
2 2
3 −Last update: 2026-11-02 (Phase 5 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·
3 +Last update: 2026-11-02 (Phase 7 passed; Phase 8 review in progress). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·
4 4 🧭 experimental · ⛔ blocked · ⏳ planned · ✖ not implemented (deliberately).
5 5
6 6 ## Phases
@@ -12,8 +12,8 @@ Last update: 2026-11-02 (Phase 5 passed). Legend: ✅ verified by tests/artifact
12 12 | 3 Numerical primitives | accuracy + measured break-even | ✅ passed 2026-11-02 | `[metal]` 6 cases / 6 411 assertions; `experiments/results/bench_primitives_summary.json` (Metal wins: fused realized ≥ 39 k elements up to 3.4×, GARCH NLL P=64 up to 7.9×; CPU wins: rolling sums, GARCH P=1, small panels) |
13 13 | 4 Econometrics (Tier A) | references + Monte Carlo | ✅ passed 2026-11-02 | R (highfrequency/rugarch) + statsmodels/arch references, `tests/simulation` Monte Carlo, `docs/methods/registry.md` |
14 14 | 5 Extensions (Tier B) | per-feature specs + tests | ✅ passed 2026-11-02 (VAR/GFEVD/DY/LW only) | `tests/reference/test_var_reference.cpp` 184 assertions vs statsmodels |
15 −| 6 Benchmarking E1–E7 | every claim traceable | ⏳ | — |
16 −| 7 Manuscript | reproducible build, no placeholders | ⏳ | — |
15 +| 6 Benchmarking E1–E7 | every claim traceable | ✅ passed 2026-11-02 | `experiments/results/raw/*.jsonl` + manifests; `key_numbers.json`; `docs/PROGRESS.md` Phase 6 |
16 +| 7 Manuscript | reproducible build, no placeholders | ✅ passed 2026-11-02 | `paper/main.pdf` 30 p., 0 undefined refs, tables/figures generated from artifacts |
17 17 | 8 Independent review | clean-checkout reproduction | ⏳ | — |
18 18
19 19 ## Methods registry (summary; full entries in `docs/methods/registry.md` from Phase 4)
@@ -34,7 +34,15 @@ Last update: 2026-11-02 (Phase 5 passed). Legend: ✅ verified by tests/artifact
34 34 - None at Phase 0. Seven cluster nodes unreachable (m2m16, M2M32, M2M32b, M4M36, m4ma, m4mb, m4mc): E7 reports them as
35 35 not tested unless they come back.
36 36
37 +## Headline measured results (laptop M5 Max unless stated; see `experiments/results/key_numbers.json`)
38 +- Metal vs CPU FP64 accuracy: realized measures ≤ 1.6e−7 relative on 233 k real session segments; bitwise reproducible.
39 +- Fused realized kernel: Metal wins from ≈ 4e4 elements, 2.0–3.4× at 4e6–4e7 (kernel level); 1.07–1.41× at the
40 + estimator level on 40 M real returns (Amdahl: FP64 post-processing and conversion).
41 +- Batched GARCH likelihood grids: 5.1× (E3, 888 × 256) to 7.9× (P = 64 microbenchmark); P = 1 → CPU wins.
42 +- Rolling sums: CPU wins everywhere (negative result). Small panels (≤ 4e5 elements): ties or CPU.
43 +- Pipeline (E6): RAID 20 M bars/s vs Polars/DuckDB 14 M, pandas 0.9 M; GPU irrelevant at that stage.
44 +- E7: GPU gains largest on weakest CPUs (M2 4.0×) and smallest on M5 (1.1×).
45 +
37 46 ## Next safe action
38 −Phase 6: experiments E1–E7 (configs in `experiments/configs/`, drivers in `benchmarks/` and `experiments/scripts/`,
39 −raw records + manifests under `experiments/results/`), starting with the E7 bundle for cluster nodes and the FinData
40 −universe/export for E1–E4.
47 +Phase 8: independent review — clean-checkout build and test (CPU-only preset and Metal preset), numerical audit of the
48 +manuscript numbers against `key_numbers.json`, license/secret scan, release checklist.
modified docs/PROGRESS.md +40 −0
@@ -157,3 +157,43 @@ panel (`datasets/fixtures/var_panel.csv`): coefficients/Σ_u/llf/orthogonalised
157 157 computation in Python) 1e−9, DY totals 1e−7, BIC order, LW shrinkage 1e−9 (`tests/reference/test_var_reference.cpp`,
158 158 184 assertions). Rolling connectedness parallel over windows (0 failures on the fixture). Other Tier B/C items are
159 159 deliberately not implemented (registry).
160 +
161 +## Phase 6 — Benchmarking E1–E7 (2026-11-02, 18:10–20:40 ET) — GATE PASSED
162 +Raw records + manifests under `experiments/results/raw/` (one JSONL per experiment, `.manifest.json` with host, versions,
163 +load, thermal, seeds, input hashes); summaries and every paper table/figure produced by
164 +`experiments/scripts/make_paper_assets.py` (hashes in `experiments/manifests/paper_assets.json`; prose numbers only from
165 +`experiments/results/key_numbers.json`).
166 +- E0: universe = seeded sample of 1 000 of the 6 046 symbols active through 2024 (14 600 coverage rows); 20 exports,
167 + 43 346 886 bars, 631 MB, dataset version 17 375, 437 s; E0b: 1.82 M daily bars 2015–2024.
168 +- E1 (estimator path, laptop): 926 symbols × 252 sessions = 40 M returns — CPU 18T 29–30 ms, Metal 20–28 ms
169 + (1.07–1.41×), ties/CPU wins ≤ 4.8 M elements; fusion gain 1.4–3.2×; max |ΔRV|/RV vs FP64 1.6e−7 (daily segments),
170 + 1.4e−8 (yearly). Synthetic 10 000 × 1 month (85.8 M): CPU 54 ms, Metal 35 ms (1.53×).
171 +- E2: HAR rolling (120-session window) on 100 symbols: median QLIKE HAR 0.196/0.146/0.134 vs RW 0.251/0.239/0.301
172 + (h = 1/5/22); HAR beats RW for 84/86/78 % of symbols. Runtime 781 series × 252 obs: per-series QR 18T 0.68 ms,
173 + batched CPU 3.9 ms, batched Metal 4.7 ms (tiny designs: GPU launch-bound).
174 +- E3: 888 symbols × ~2 459 daily returns: convergence GARCH 100 %, GJR 98.4 %, EGARCH 92.8 %, GARCH-t 100 %
175 + (after ≤ 2 restarts); 2.9–18 ms per fit; median QLIKE of fixed-parameter 1-day forecasts vs RV 0.39–0.40 against
176 + 0.27–0.28 for the RV random walk. GPU grid 888 × 256 parameter vectors: Metal 23 ms vs CPU 18T 117 ms (5.1×),
177 + argmin identical 888/888, max rel. NLL difference 2e−3 at boundary grid points.
178 +- E4: realized covariance (5-min synchronised) N = 10/30/60/100: median condition number 81/422/5.9e3/singular (N > 78
179 + bins); LW shrinkage 0.16–0.33; rolling DY connectedness 133 windows in 0.5/2.3/8.9/29 ms, 0 failures.
180 +- E5 (R = 1 000): GARCH n = 2 000 coverage 0.93–0.97, |bias| ≤ 0.005, 1 000/1 000 converged; n = 500 β bias −0.026,
181 + α coverage 0.90; HAR HAC coverage 0.94 (h = 1), 0.90–0.94 (h = 5); bitwise reproducibility across threads and Metal
182 + runs; Metal vs CPU RV 3.7e−8.
183 +- E6: per 2.37 M-bar export file — RAID CPU 0.118 s (20 M bars/s), RAID Metal 0.125 s, Polars 0.165 s, DuckDB 0.164 s,
184 + pandas 2.56 s; read 0.065 s, prep 0.021 s, estimate 0.031 s (CPU) / 0.037 s (Metal). Column projection took the
185 + pipeline from 0.35 s to 0.12 s. Baselines: approximate early-close rule (no exchange calendar in those engines);
186 + bugs fixed on the way: DuckDB 2.0 API, Polars i8 overflow in hour×60.
187 +- E7 (11 nodes, M2 → M6): all Metal tests pass with prebuilt metallib and runtime MSL; cold compile 37–49 ms (110 ms on
188 + the 8 GB M2), warm 0.3–0.6 ms; RV fused 1000×3900 speedup 4.0× (M2) … 1.1× (M5 Max/Pro); GARCH P=64 7.8× (M2 Max) …
189 + 1.8× (M5 Pro); rolling 0.2–0.65× everywhere.
190 +- Engineering findings during Phase 6 (recorded): serial tripower/post-processing diluted E1 (fixed: parallel, cbrt);
191 + Metal backend recreated per call through an expired weak_ptr (fixed: process singleton); E3 evaluation index bug with
192 + the longer daily history (fixed); per-series FP32 scaling in the GARCH kernel (max rel. error on real grids 6.8e−4 →
193 + 2e−3 at boundary points only, argmin agreement 887 → 888/888).
194 +
195 +## Phase 7 — Manuscript (2026-11-02, 20:40–21:30 ET) — GATE PASSED
196 +`paper/main.tex` + 13 sections + appendices; 30 pages; 57 BibTeX entries all resolved on Crossref (DOI content
197 +negotiation) or hand-verified; `latexmk` exit 0, **0 undefined citations/references**; all tables `\input` from
198 +`paper/tables/` and figures from `paper/figures/`, both generated by `make_paper_assets.py` from tracked artifacts.
199 +Known cosmetic overfull boxes in two listings; no placeholder, no hand-typed number.
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modified paper/references.bib +39 −39
@@ -1,82 +1,82 @@
1 1 % references.bib — every entry resolved on Crossref (doi.org content negotiation) on 2026-11-02; software entries below are hand-written with version and URL.
2 2
3 −@article{AndersenBollerslevDieboldLabys2003, title={Modeling and Forecasting Realized Volatility}, volume={71}, ISSN={1468-0262}, url={http://dx.doi.org/10.1111/1468-0262.00418}, DOI={10.1111/1468-0262.00418}, number={2}, journal={Econometrica}, publisher={The Econometric Society}, author={Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Labys, Paul}, year={2003}, month=Mar, pages={579–625} }
3 +@article{AndersenBollerslevDieboldLabys2003, title={Modeling and Forecasting Realized Volatility}, volume={71}, ISSN={1468-0262}, url={http://dx.doi.org/10.1111/1468-0262.00418}, DOI={10.1111/1468-0262.00418}, number={2}, journal={Econometrica}, publisher={The Econometric Society}, author={Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Labys, Paul}, year={2003}, pages={579–625} }
4 4
5 −@article{BarndorffNielsenShephard2004, title={Power and Bipower Variation with Stochastic Volatility and Jumps}, volume={2}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbh001}, DOI={10.1093/jjfinec/nbh001}, number={1}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Barndorff-Nielsen, O. E.}, year={2004}, month=Dec, pages={1–37} }
5 +@article{BarndorffNielsenShephard2004, title={Power and Bipower Variation with Stochastic Volatility and Jumps}, volume={2}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbh001}, DOI={10.1093/jjfinec/nbh001}, number={1}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Barndorff-Nielsen, O. E.}, year={2004}, pages={1–37} }
6 6
7 −@article{BarndorffNielsenShephard2006, title={Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation}, volume={4}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbi022}, DOI={10.1093/jjfinec/nbi022}, number={1}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Barndorff-Nielsen, O. E.}, year={2005}, month=Aug, pages={1–30} }
7 +@article{BarndorffNielsenShephard2006, title={Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation}, volume={4}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbi022}, DOI={10.1093/jjfinec/nbi022}, number={1}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Barndorff-Nielsen, O. E.}, year={2005}, pages={1–30} }
8 8
9 −@article{Corsi2009, title={A Simple Approximate Long-Memory Model of Realized Volatility}, volume={7}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbp001}, DOI={10.1093/jjfinec/nbp001}, number={2}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Corsi, F.}, year={2008}, month=Nov, pages={174–196} }
9 +@article{Corsi2009, title={A Simple Approximate Long-Memory Model of Realized Volatility}, volume={7}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbp001}, DOI={10.1093/jjfinec/nbp001}, number={2}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Corsi, F.}, year={2008}, pages={174–196} }
10 10
11 −@article{Bollerslev1986, title={Generalized autoregressive conditional heteroskedasticity}, volume={31}, ISSN={0304-4076}, url={http://dx.doi.org/10.1016/0304-4076(86)90063-1}, DOI={10.1016/0304-4076(86)90063-1}, number={3}, journal={Journal of Econometrics}, publisher={Elsevier BV}, author={Bollerslev, Tim}, year={1986}, month=Apr, pages={307–327} }
11 +@article{Bollerslev1986, title={Generalized autoregressive conditional heteroskedasticity}, volume={31}, ISSN={0304-4076}, url={http://dx.doi.org/10.1016/0304-4076(86)90063-1}, DOI={10.1016/0304-4076(86)90063-1}, number={3}, journal={Journal of Econometrics}, publisher={Elsevier BV}, author={Bollerslev, Tim}, year={1986}, pages={307–327} }
12 12
13 −@article{Engle1982, title={Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation}, volume={50}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1912773}, DOI={10.2307/1912773}, number={4}, journal={Econometrica}, publisher={JSTOR}, author={Engle, Robert F.}, year={1982}, month=July, pages={987} }
13 +@article{Engle1982, title={Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation}, volume={50}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1912773}, DOI={10.2307/1912773}, number={4}, journal={Econometrica}, publisher={JSTOR}, author={Engle, Robert F.}, year={1982}, pages={987} }
14 14
15 −@article{GlostenJagannathanRunkle1993, title={On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks}, volume={48}, ISSN={1540-6261}, url={http://dx.doi.org/10.1111/j.1540-6261.1993.tb05128.x}, DOI={10.1111/j.1540-6261.1993.tb05128.x}, number={5}, journal={The Journal of Finance}, publisher={Wiley}, author={GLOSTEN, LAWRENCE R. and JAGANNATHAN, RAVI and RUNKLE, DAVID E.}, year={1993}, month=Dec, pages={1779–1801} }
15 +@article{GlostenJagannathanRunkle1993, title={On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks}, volume={48}, ISSN={1540-6261}, url={http://dx.doi.org/10.1111/j.1540-6261.1993.tb05128.x}, DOI={10.1111/j.1540-6261.1993.tb05128.x}, number={5}, journal={The Journal of Finance}, publisher={Wiley}, author={GLOSTEN, LAWRENCE R. and JAGANNATHAN, RAVI and RUNKLE, DAVID E.}, year={1993}, pages={1779–1801} }
16 16
17 −@article{Nelson1991, title={Conditional Heteroskedasticity in Asset Returns: A New Approach}, volume={59}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/2938260}, DOI={10.2307/2938260}, number={2}, journal={Econometrica}, publisher={JSTOR}, author={Nelson, Daniel B.}, year={1991}, month=Mar, pages={347} }
17 +@article{Nelson1991, title={Conditional Heteroskedasticity in Asset Returns: A New Approach}, volume={59}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/2938260}, DOI={10.2307/2938260}, number={2}, journal={Econometrica}, publisher={JSTOR}, author={Nelson, Daniel B.}, year={1991}, pages={347} }
18 18
19 −@article{NeweyWest1987, title={A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix}, volume={55}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1913610}, DOI={10.2307/1913610}, number={3}, journal={Econometrica}, publisher={JSTOR}, author={Newey, Whitney K. and West, Kenneth D.}, year={1987}, month=May, pages={703} }
19 +@article{NeweyWest1987, title={A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix}, volume={55}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1913610}, DOI={10.2307/1913610}, number={3}, journal={Econometrica}, publisher={JSTOR}, author={Newey, Whitney K. and West, Kenneth D.}, year={1987}, pages={703} }
20 20
21 −@article{White1980, title={A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity}, volume={48}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1912934}, DOI={10.2307/1912934}, number={4}, journal={Econometrica}, publisher={JSTOR}, author={White, Halbert}, year={1980}, month=May, pages={817} }
21 +@article{White1980, title={A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity}, volume={48}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1912934}, DOI={10.2307/1912934}, number={4}, journal={Econometrica}, publisher={JSTOR}, author={White, Halbert}, year={1980}, pages={817} }
22 22
23 −@article{BollerslevPattonQuaedvlieg2016, title={Exploiting the errors: A simple approach for improved volatility forecasting}, volume={192}, ISSN={0304-4076}, url={http://dx.doi.org/10.1016/j.jeconom.2015.10.007}, DOI={10.1016/j.jeconom.2015.10.007}, number={1}, journal={Journal of Econometrics}, publisher={Elsevier BV}, author={Bollerslev, Tim and Patton, Andrew J. and Quaedvlieg, Rogier}, year={2016}, month=May, pages={1–18} }
23 +@article{BollerslevPattonQuaedvlieg2016, title={Exploiting the errors: A simple approach for improved volatility forecasting}, volume={192}, ISSN={0304-4076}, url={http://dx.doi.org/10.1016/j.jeconom.2015.10.007}, DOI={10.1016/j.jeconom.2015.10.007}, number={1}, journal={Journal of Econometrics}, publisher={Elsevier BV}, author={Bollerslev, Tim and Patton, Andrew J. and Quaedvlieg, Rogier}, year={2016}, pages={1–18} }
24 24
25 −@article{HansenHuangShek2012, title={Realized GARCH: a joint model for returns and realized measures of volatility}, volume={27}, ISSN={1099-1255}, url={http://dx.doi.org/10.1002/jae.1234}, DOI={10.1002/jae.1234}, number={6}, journal={Journal of Applied Econometrics}, publisher={Wiley}, author={Hansen, Peter Reinhard and Huang, Zhuo and Shek, Howard Howan}, year={2011}, month=Mar, pages={877–906} }
25 +@article{HansenHuangShek2012, title={Realized GARCH: a joint model for returns and realized measures of volatility}, volume={27}, ISSN={1099-1255}, url={http://dx.doi.org/10.1002/jae.1234}, DOI={10.1002/jae.1234}, number={6}, journal={Journal of Applied Econometrics}, publisher={Wiley}, author={Hansen, Peter Reinhard and Huang, Zhuo and Shek, Howard Howan}, year={2011}, pages={877–906} }
26 26
27 −@article{DieboldYilmaz2012, title={Better to give than to receive: Predictive directional measurement of volatility spillovers}, volume={28}, ISSN={0169-2070}, url={http://dx.doi.org/10.1016/j.ijforecast.2011.02.006}, DOI={10.1016/j.ijforecast.2011.02.006}, number={1}, journal={International Journal of Forecasting}, publisher={Elsevier BV}, author={Diebold, Francis X. and Yilmaz, Kamil}, year={2012}, month=Jan, pages={57–66} }
27 +@article{DieboldYilmaz2012, title={Better to give than to receive: Predictive directional measurement of volatility spillovers}, volume={28}, ISSN={0169-2070}, url={http://dx.doi.org/10.1016/j.ijforecast.2011.02.006}, DOI={10.1016/j.ijforecast.2011.02.006}, number={1}, journal={International Journal of Forecasting}, publisher={Elsevier BV}, author={Diebold, Francis X. and Yilmaz, Kamil}, year={2012}, pages={57–66} }
28 28
29 −@article{DieboldYilmaz2014, title={On the network topology of variance decompositions: Measuring the connectedness of financial firms}, volume={182}, ISSN={0304-4076}, url={http://dx.doi.org/10.1016/j.jeconom.2014.04.012}, DOI={10.1016/j.jeconom.2014.04.012}, number={1}, journal={Journal of Econometrics}, publisher={Elsevier BV}, author={Diebold, Francis X. and Yılmaz, Kamil}, year={2014}, month=Sept, pages={119–134} }
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79 −@misc{Ghalanos2024rugarch, title={rugarch: Univariate GARCH Models}, url={http://dx.doi.org/10.32614/cran.package.rugarch}, DOI={10.32614/cran.package.rugarch}, journal={CRAN: Contributed Packages}, publisher={The R Foundation}, author={Galanos, Alexios}, year={2011}, month=Sept }
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80 80
81 81
82 82 @misc{Arrow2025, title={Apache Arrow: a cross-language development platform for in-memory analytics, C++ library version 26.0.0}, author={{Apache Software Foundation}}, year={2025}, howpublished={\url{https://arrow.apache.org/}}, note={Accessed 2026-11-02}}
modified paper/sections/applications.tex +3 −3
@@ -15,7 +15,7 @@ The applications are not forecasting studies; they show that the batched estimat
15 15 \centering\small
16 16 \caption{E2 --- runtime of HAR-RV estimation ($h=1$), milliseconds (medians of 5 repetitions).}
17 17 \label{tab:e2rt}
18 −\input{tables/tab_e2_runtime}
18 +\resizebox{\textwidth}{!}{\input{tables/tab_e2_runtime}}
19 19 \end{table}
20 20
21 21 \paragraph{E3 --- GARCH-family panel.} GARCH(1,1), GJR, EGARCH and GARCH-$t$ are fitted by QML to the daily close-to-close log returns of 888 symbols (2015--2024 daily bars, median 2\,459 training observations; the last 40 sessions of 2024 are held out). Table~\ref{tab:e3} reports convergence rates, iterations, time per fit, persistence, and the QLIKE of the fixed-parameter one-day-ahead variance forecasts against the next day's realized variance. GARCH and GARCH-$t$ converge for all 888 series, GJR for 98.4\,\% and EGARCH for 92.8\,\% (after up to two restarts; the failures are reported as such, not as estimates), in 2.9--18\,ms per fit; persistence medians are 0.956--0.973. Daily GARCH forecasts have a median QLIKE of 0.39--0.40 against 0.27--0.28 for the realized-variance random walk: a one-day-ahead forecast built from intraday data beats one built from daily returns, as the literature since \citet{AndersenBollerslevDieboldLabys2003} would predict, and the gap is not a numerical artefact. The GPU's contribution in E3 is the likelihood grid: evaluating 256 $(\omega,\alpha,\beta)$ combinations per series for all 888 series takes 23\,ms on Metal against 117\,ms on 18 CPU threads (5.1$\times$); the grid argmin is identical on both backends for all 888 series, with a maximum relative difference of $2\times10^{-3}$ in the likelihood at the least-likely grid points (near the non-stationarity boundary).
@@ -24,7 +24,7 @@ The applications are not forecasting studies; they show that the batched estimat
24 24 \centering\small
25 25 \caption{E3 --- GARCH-family QML on 888 daily return series (2015--2024); forecasts evaluated on the last 40 sessions of 2024 against realized variance.}
26 26 \label{tab:e3}
27 −\input{tables/tab_e3_fits}
27 +\resizebox{\textwidth}{!}{\input{tables/tab_e3_fits}}
28 28 \end{table}
29 29
30 30 \paragraph{E4 --- realized covariance and connectedness.} For $N \in \{10, 30, 60, 100\}$ symbols with at least 95\,\% regular-bar coverage, daily realized covariance matrices are formed from synchronised 5-minute returns (78 per day) on the days where every symbol has the full grid, and rolling Diebold--Yilmaz total connectedness is computed from a VAR(1) on the daily log-RV panel (120-day windows, $H = 10$). Table~\ref{tab:e4} shows the two constraints the charter asked for. Memory is not one of them: the rolling connectedness over 133 windows takes 0.5, 2.3, 8.9 and 29\,ms for $N = 10, 30, 60, 100$ on the CPU and never fails. Conditioning is: the median condition number of the daily realized covariance grows from 81 ($N = 10$) to 422 ($N = 30$) and $5.9\times10^3$ ($N = 60$), and the matrix is singular for $N = 100 > 78$ bins; the Ledoit--Wolf shrinkage intensity rises from 0.16 to 0.33 accordingly. Strict synchronisation also discards 70--164 of the 252 days as $N$ grows. Connectedness itself is not GPU work at these sizes; the GPU-relevant part is the realized covariance of large panels, which reduces to the batched sufficient statistics of E1.
@@ -33,5 +33,5 @@ The applications are not forecasting studies; they show that the batched estimat
33 33 \centering\small
34 34 \caption{E4 --- daily realized covariance (5-minute, synchronised) and rolling Diebold--Yilmaz connectedness, 2024.}
35 35 \label{tab:e4}
36 −\input{tables/tab_e4}
36 +\resizebox{\textwidth}{!}{\input{tables/tab_e4}}
37 37 \end{table}
modified paper/sections/architecture.tex +1 −1
@@ -5,7 +5,7 @@
5 5
6 6 \begin{figure}[t]
7 7 \centering
8 −\begin{lstlisting}[basicstyle=\ttfamily\scriptsize]
8 +\begin{lstlisting}[basicstyle=\ttfamily\tiny]
9 9 Python (nanobind, GIL released) raid.api / raid.findata CLI: raid devices|validate|estimate|data
10 10 ------------------------------------------------------------------------------------------------------
11 11 core types (Timestamp us UTC, Date, Interval, Backend, Precision) | RaidError | log (redaction)
modified paper/sections/correctness.tex +8 −3
@@ -4,11 +4,11 @@
4 4 Every Tier~A method satisfies five requirements: an independent FP64 CPU reference, an analytical or simulation truth where one exists, agreement with established software under identical conventions, GPU/CPU agreement within a documented tolerance, and adversarial tests. Table~\ref{tab:validation} summarises the reference comparisons on committed synthetic fixtures (no vendor data); every row is a test in the repository that runs on every build.
5 5
6 6 \begin{table}[t]
7 −\centering\small
7 +\centering\scriptsize
8 8 \begin{threeparttable}
9 9 \caption{Reference validation on synthetic fixtures (all tests pass).}
10 10 \label{tab:validation}
11 −\begin{tabular}{lllr}
11 +\begin{tabular}{p{3.6cm}p{3.6cm}p{5.2cm}p{3cm}}
12 12 \toprule
13 13 Method & Reference (version) & Quantity compared & Tolerance \\
14 14 \midrule
@@ -34,7 +34,12 @@ Metal vs CPU FP64 & \raid{} CPU backend & RV, BPV, RSV$^\pm$ ($n$ = 390--39\,000
34 34
35 35 \paragraph{Monte Carlo.} Table~\ref{tab:e5} (experiment E5, $R = 1\,000$ replications) reports bias, RMSE and the empirical coverage of 95\,\% intervals. For GARCH(1,1) with $(\omega,\alpha,\beta) = (0.02, 0.08, 0.90)$ and $n = 2\,000$, biases are at most $0.005$ in absolute value, coverage of the QMLE intervals is 0.93--0.97, and all 1\,000 fits converge; at $n = 500$ the familiar finite-sample downward bias of $\beta$ ($-0.026$) and under-coverage of $\alpha$ (0.90) appear. For HAR with overlapping $h = 5$ targets and HAC inference, coverage of the pseudo-true projection coefficients is 0.90--0.94 ($T = 1\,200$), the usual mild under-coverage of HAC. Realized variance converges at the $\sqrt{2/M}$ rate: the Monte Carlo RMSE is within 10\,\% of $\sqrt{2/M}\,\mathrm{IV}$ for $M \in \{39, 390, 3\,900\}$. The stationary-bootstrap interval for the mean of an AR(1) covers in 89\,\% of replications ($R = 100$, $n = 800$, $b = 10$).
36 36
37 −\input{tables/tab_e5}
37 +\begin{table}[t]
38 +\centering\small
39 +\caption{E5 --- Monte Carlo bias, RMSE and 95\,\% coverage ($R = 1\,000$; HAR coverage listed for the four coefficients).}
40 +\label{tab:e5}
41 +\resizebox{\textwidth}{!}{\input{tables/tab_e5}}
42 +\end{table}
38 43
39 44 \paragraph{Reproducibility.} With the same seed, the 2\,000 bootstrap statistics are bitwise identical when computed with 1, 4 or 18 threads; the CPU realized measures are bitwise identical with 1 or 18 threads; two Metal runs give bitwise identical RV, BPV and RQ; and the maximum relative difference between Metal and CPU FP64 realized variance on 50 segments of Student-$t(5)$ returns is $3.7\times10^{-8}$, consistent with the input-rounding bound of Section~\ref{sec:metal}.
40 45
modified paper/sections/endtoend.tex +2 −2
@@ -7,7 +7,7 @@
7 7 \centering\scriptsize
8 8 \caption{E1 --- batched realized measures (estimator path), laptop. Medians of 5 repetitions; ``real'' = 2024 FinData panel; ``synthetic'' = Student-$t(5)$ returns; max rel.\ err.\ = largest $|\RV_{\text{Metal}}-\RV_{\text{FP64}}|/\RV_{\text{FP64}}$ over segments.}
9 9 \label{tab:e1}
10 −\input{tables/tab_e1}
10 +\resizebox{\textwidth}{!}{\input{tables/tab_e1}}
11 11 \end{table}
12 12
13 13 \begin{figure}[t]
@@ -22,5 +22,5 @@
22 22 \centering\small
23 23 \caption{E6 --- end-to-end pipeline per export file (median of 4 files $\times$ 3 repetitions; 2.37 million bars per file).}
24 24 \label{tab:e6}
25 −\input{tables/tab_e6}
25 +\resizebox{\textwidth}{!}{\input{tables/tab_e6}}
26 26 \end{table}
modified paper/sections/microbenchmarks.tex +2 −2
@@ -7,7 +7,7 @@
7 7 \centering\scriptsize
8 8 \caption{Primitive kernels, laptop (M5 Max). Medians of wall-clock milliseconds over 5 repetitions; CPU MT uses 18 threads; speedup $= T_{\text{CPU MT}}/T_{\text{Metal}}$; verdict by non-overlapping bootstrap CIs.}
9 9 \label{tab:prim}
10 −\input{tables/tab_primitives}
10 +\resizebox{\textwidth}{!}{\input{tables/tab_primitives}}
11 11 \end{table}
12 12
13 13 \begin{figure}[t]
@@ -26,7 +26,7 @@ Four findings answer RQ1 at the kernel level. First, the fused realized kernel i
26 26 \centering\scriptsize
27 27 \caption{E7 --- generation sweep (3 repetitions, shuffled; speedups are CPU MT / Metal medians at the stated shape; tests = Metal test suite with the prebuilt metallib / with runtime MSL compilation).}
28 28 \label{tab:e7}
29 −\input{tables/tab_e7}
29 +\resizebox{\textwidth}{!}{\input{tables/tab_e7}}
30 30 \end{table}
31 31
32 32 \begin{figure}[t]
33 33
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