WP46 paper: genealogy figure in the taxonomy section, encyclopedic appendix
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paper/appendices/formulas.tex
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| 1 | +\section{The GARCH family: an encyclopedic table}\label{app:encyclopedia} | ||||
| 2 | + | ||||
| 3 | +Table~\ref{tab:encyclopedia} lists every architecture of Figure~\ref{fig:genealogy} with its seminal reference, its defining | ||||
| 4 | +variance equation in the notation of Section~\ref{sec:taxonomy}, what it adds to its parent, and its status in this paper | ||||
| 5 | +(scored, extension, unsupported, or out of scope with the reason). Nomenclature traps---which packages call the Zakoïan model | ||||
| 6 | +``TGARCH'' and which call GJR ``TARCH'', the three EGARCH parameterizations, NGARCH versus NAGARCH, APARCH versus PGARCH---are | ||||
| 7 | +documented in the replication package (\texttt{docs/genealogy\_notes.md}). | ||||
| 8 | + | ||||
| 9 | +{\footnotesize\input{tables/tab_encyclopedia}} | ||||
| 10 | + | ||||
| 1 | \section{Complete specifications, admissibility conditions and forecast recursions}\label{app:formulas} | 11 | \section{Complete specifications, admissibility conditions and forecast recursions}\label{app:formulas} | ||
| 2 | 12 | ||||
| 3 | This appendix states, for every scored architecture, the recursion, the parameter space enforced by the optimizer, the | 13 | This appendix states, for every scored architecture, the recursion, the parameter space enforced by the optimizer, the | ||
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paper/main.pdf
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paper/sections/taxonomy.tex
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| 1 | \section{A unified taxonomy and mathematical framework}\label{sec:taxonomy} | 1 | \section{A unified taxonomy and mathematical framework}\label{sec:taxonomy} | ||
| 2 | 2 | ||||
| 3 | +Figure~\ref{fig:genealogy} places the family on a single map: sixty-four architectures from 1982 to 2026, arranged by | ||||
| 4 | +family and by the year of their seminal reference, with the nesting or extension relations drawn as arrows; filled markers | ||||
| 5 | +are the architectures scored in the pre-registered benchmark, half-filled markers the seven post-registration extensions, and | ||||
| 6 | +hollow markers the variants that are inventoried but not scored (with the reason recorded in the encyclopedic table of | ||||
| 7 | +Appendix~\ref{app:encyclopedia}). The map makes two things visible at once: almost everything descends from GARCH(1,1) | ||||
| 8 | +through a handful of operations---asymmetric news impact, power transformation, fractional differencing, component | ||||
| 9 | +decomposition, regime switching, score-driven updating, and the replacement of the squared return by a realized measure---and | ||||
| 10 | +the multivariate branch grew in parallel from the same operations applied to covariance matrices. | ||||
| 11 | + | ||||
| 12 | +\begin{figure}[tp]\centering | ||||
| 13 | +\includegraphics[width=\textwidth]{figures/fig_genealogy.pdf} | ||||
| 14 | +\caption{Genealogy of the ARCH/GARCH family, 1982--2026. Rows are families, the horizontal position is the year of the seminal | ||||
| 15 | +reference, arrows run from a parent to the model that nests or extends it. Filled: scored in the pre-registered benchmark; | ||||
| 16 | +half-filled (thick edge): post-registration extension; hollow: inventoried, not scored. Generated from | ||||
| 17 | +\texttt{results/manifests/garch\_genealogy.yaml} (64 entries; references in Appendix~\ref{app:encyclopedia}).}\label{fig:genealogy} | ||||
| 18 | +\end{figure} | ||||
| 19 | + | ||||
| 3 | Throughout, $r_t$ is the daily log return in percent, $\F_{t}$ the information set at the close of day $t$, | 20 | Throughout, $r_t$ is the daily log return in percent, $\F_{t}$ the information set at the close of day $t$, | ||
| 4 | $r_t=\mu+\varepsilon_t$ with $\varepsilon_t=\sigma_t z_t$, $z_t\,|\,\F_{t-1}\sim D(0,1;\bm\eta)$ a standardized | 21 | $r_t=\mu+\varepsilon_t$ with $\varepsilon_t=\sigma_t z_t$, $z_t\,|\,\F_{t-1}\sim D(0,1;\bm\eta)$ a standardized | ||
| 5 | innovation with distribution parameters $\bm\eta$, and $\sigma_t^2=\Var(r_t\,|\,\F_{t-1})$ in percent$^2$. Every model | 22 | innovation with distribution parameters $\bm\eta$, and $\sigma_t^2=\Var(r_t\,|\,\F_{t-1})$ in percent$^2$. Every model | ||
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progress.md
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@@ -76,3 +76,7 @@ All times ET. "Done" means executed with the listed command and artefact; "plann | |||||
| 76 | in `src/wp46/models/extensions.py`, registry status `extension`; tests `tests/unit/test_extensions.py` (6 passed: fractional | 76 | in `src/wp46/models/extensions.py`, registry status `extension`; tests `tests/unit/test_extensions.py` (6 passed: fractional | ||
| 77 | weights, HYGARCH(amp=1) reproduces arch's FIGARCH likelihood, FIAPARCH/ST-GARCH/GARCH-MIDAS nest FIGARCH/GARCH, seeded simulation, | 77 | weights, HYGARCH(amp=1) reproduces arch's FIGARCH likelihood, FIAPARCH/ST-GARCH/GARCH-MIDAS nest FIGARCH/GARCH, seeded simulation, | ||
| 78 | no look-ahead). Scored with the frozen protocol but reported separately from the pre-registered set (job list `jobs_ext.json`). | 78 | no look-ahead). Scored with the frozen protocol but reported separately from the pre-registered set (job list `jobs_ext.json`). | ||
| 79 | +- **Synthesis deliverables (2026-11-09 night):** `results/manifests/garch_genealogy.yaml` (64 architectures: 25 scored, 7 extension, | ||||
| 80 | + 2 unsupported, 30 out of scope with reasons), `scripts/make_genealogy_figure.py` → `paper/figures/fig_genealogy.pdf` (Figure 1 of the | ||||
| 81 | + taxonomy section), `scripts/make_encyclopedia.py` → `paper/tables/tab_encyclopedia.tex` (Appendix), `docs/genealogy_notes.md` | ||||
| 82 | + (nomenclature traps and package naming); 13 seminal references added and Crossref-verified (218 entries in references.bib). | ||||
| 79 | 83 | ||||