spb/wp46_uqo

1# WP46 — Literature matrix (Phase 0)23**Status:** Phase 0 deliverable (literature inventory). Literature cutoff **2026-11-09**. Every bibkey below exists in4`paper/references.bib`, which is generated by `scripts/build_references.py` **only** from records whose title was5verified against Crossref (193), arXiv (5) or OpenAlex (2), plus five items with no registry record that were6confirmed by fetching a publisher/NBER/RePEc/Zenodo/MSCI page (`manual (URL fetched)`). Per-key evidence (identifier,7fetched title, date, source) is in `results/metrics/references_verification.json`; the single unverified candidate is in8`results/metrics/references_unverified.json` and is **not** cited anywhere.910Counts (run of 2026-11-09): 206 candidates → 205 entries written to the .bib (200 registry-verified: 193 Crossref,115 arXiv, 2 OpenAlex; + 5 manual-URL), 1 unverified and excluded: `chung1999estimating`.1213**Scope column.** "Planned scope" is the *intended* implementation route for WP46 and is **not** a completion claim; the14binding list is `configs/model_registry.yaml` once frozen by the pre-registered protocol. Routes: `arch` (Python `arch`158.0.0, `sheppard2025arch`), `rugarch` (R 1.5-6, `galanos2011rugarch`), `rmgarch` (`galanos2013rmgarch`), `MSGARCH`16(`ardia2016msgarch`), `highfrequency` (`boudt2012highfrequency`), `custom` (own implementation, must pass the17stronger tests of CLAUDE.md rule 6), `extension` (clearly labelled non-GARCH / ML extension), `out of scope`.1819Conventions: $r_t = \mu_t + \varepsilon_t$, $\varepsilon_t = \sigma_t z_t$, $z_t \sim$ i.i.d. $(0,1)$; $h_t=\sigma_t^2$.20Daily log returns are in **percent** (CLAUDE.md rule 4), so $h_t$ is in percent².2122---2324## (a) Univariate ARCH/GARCH architectures2526### a.1 Classical2728| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |29|---|---|---|---|---|30| `engle1982autoregressive` | ARCH(q): $h_t=\omega+\sum_{i=1}^q\alpha_i\varepsilon_{t-i}^2$ | Conditional heteroskedasticity as an AR in squared shocks; LM test; UK inflation application | Positivity $\omega>0,\alpha_i\ge0$; covariance stationarity $\sum\alpha_i<1$; large $q$ needed in practice → motivates GARCH | arch (`ARCH`), rugarch (sGARCH with $p=0$); orders fixed by the protocol |31| `bollerslev1986generalized` | GARCH(p,q): $h_t=\omega+\sum\alpha_i\varepsilon_{t-i}^2+\sum\beta_j h_{t-j}$ | Parsimonious ARMA-type variance dynamics; the WP46 baseline is GARCH(1,1) | Bollerslev's $(p,q)$ order convention is (GARCH lags, ARCH lags); `arch` uses `p`=ARCH, `q`=GARCH — record the convention per package. Sufficient positivity $\omega>0,\alpha_i,\beta_j\ge0$ is not necessary for $p,q>1$ (`nelson1992inequality`) | arch, rugarch (cross-check fixture) |32| `engle1986modelling` | IGARCH: $\sum\alpha_i+\sum\beta_j=1$ | Persistence of conditional variances; integrated case still strictly stationary with finite unconditional *conditional* variance absent | Unconditional variance does not exist; forecasts grow linearly in $h$; strict stationarity still holds (`nelson1990stationarity`); QMLE asymptotics in `lumsdaine1996consistency`, `jensen2004asymptotic` | rugarch (`iGARCH`); arch via fixed constraint (custom wrapper) |33| `engle1987estimating` | ARCH-M / GARCH-M: $\mu_t = \mu + \lambda g(h_t)$ | Risk premium in the conditional mean | $g(\cdot)$ varies ($h_t$, $\sqrt{h_t}$, $\log h_t$); mean and variance parameters not separable → affects multi-step forecasts of cumulative returns | rugarch (`archm`); low priority in a variance-forecast benchmark (mean effect on $h$-day variance is second order) |34| `lamoureux1990persistence`, `mikosch2004nonstationarities`, `hillebrand2005neglecting` | Structural change ⇒ spurious IGARCH | Explains near-unit persistence by neglected breaks | Motivates the regime block and rolling windows; not a model | diagnostics only |35| `jpmorgan1996riskmetrics` | EWMA / RiskMetrics: $h_t=\lambda h_{t-1}+(1-\lambda)\varepsilon_{t-1}^2$, $\lambda=0.94$ (daily) | Industry baseline; no estimation | Zero-intercept IGARCH(1,1); same forecast at all horizons (flat term structure); 1996 Technical Document, 4th ed. (manual-URL entry, MSCI PDF) | arch (`EWMA`), fixed $\lambda$ = baseline |36| `zumbach2009riskmetrics` | RM2006: multi-horizon EWMA mixture with logarithmic decay | Long-memory-like kernel without estimation | SSRN posting (2009) of the 2007 RiskMetrics Group document; cite as working paper | custom (simple weights); optional baseline |37| `engle2001garch`, `engle2004risk`, `bollerslev1992arch`, `bollerslev1994arch`, `terasvirta2009introduction`, `bollerslev2010glossary`, `engle2001what`, `francq2019garch`, `bauwens2012handbook` | Surveys / textbooks / glossary | Nomenclature authority for the taxonomy (C1) | `bollerslev2010glossary` is the reference for acronym disambiguation; `francq2019garch` for regularity conditions | taxonomy references |3839### a.2 Asymmetric and power4041| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |42|---|---|---|---|---|43| `nelson1991conditional` | EGARCH: $\log h_t=\omega+\sum\beta_j\log h_{t-j}+\sum\alpha_i g(z_{t-i})$, $g(z)=\theta z+\gamma(|z|-E|z|)$ | Log-variance (no positivity constraints), sign and size asymmetry, GED innovations | $E|z|$ depends on the innovation law (GED/t/normal), so the intercept is distribution-specific; stationarity is $|\beta|<1$, **not** $\alpha+\beta<1$; multi-step forecasts of $h_{t+k}$ require $E[\exp(\cdot)]$ (no closed form for $k>1$ under t/GED → simulation or log-normal approximations; `arch` uses simulation/bootstrap) | arch (`EGARCH`), rugarch (`eGARCH`) — **parameterisations differ** (rugarch writes $\alpha z+\gamma(|z|-E|z|)$; arch writes $\gamma$ on $|z|-E|z|$ and $\theta$ on $z$ in the opposite order of labels); map explicitly in the model card |44| `glosten1993relation` | GJR-GARCH: $h_t=\omega+(\alpha+\gamma\mathbb{1}_{\varepsilon_{t-1}<0})\varepsilon_{t-1}^2+\beta h_{t-1}$ | Leverage via indicator on **variance** | Persistence $\alpha+\beta+\gamma\kappa$ with $\kappa=P(z<0)$ ($=1/2$ for symmetric $z$); positivity $\alpha+\gamma\ge0$. In `arch` this is `GARCH(p, o, q)` with $o>0$; in EViews "TARCH" = GJR | arch, rugarch (`gjrGARCH`) |45| `zakoian1994threshold` | TGARCH (Zakoïan): $\sigma_t=\omega+\alpha^+\varepsilon_{t-1}^+-\alpha^-\varepsilon_{t-1}^-+\beta\sigma_{t-1}$ | Threshold on the conditional **standard deviation** | **Not the same as GJR**: threshold acts on $\sigma_t$ (power 1), with separate slopes for positive and negative parts; rugarch `fGARCH(TGARCH)` follows Zakoïan; several packages/papers call GJR "TGARCH" — WP46 uses "TGARCH" only for the Zakoïan form (C1 rule: never silently equate) | rugarch (`fGARCH`, submodel `TGARCH`) |46| `ding1993long` | APARCH: $\sigma_t^\delta=\omega+\sum\alpha_i(|\varepsilon_{t-i}|-\gamma_i\varepsilon_{t-i})^\delta+\sum\beta_j\sigma_{t-j}^\delta$ | Power $\delta$ estimated; nests GARCH ($\delta=2,\gamma=0$), AVGARCH ($\delta=1,\gamma=0$), TGARCH-Zakoïan ($\delta=1$), GJR ($\delta=2$), NGARCH-Higgins–Bera | $|\gamma_i|<1$, $\delta>0$; moment conditions in `ling2002necessary`; multi-step forecast of $h$ not closed-form when $\delta\ne2$ | arch (`APARCH`), rugarch (`apARCH`) |47| `taylor2008modelling`, `schwert1989why` | AVGARCH / Taylor–Schwert: $\sigma_t=\omega+\alpha|\varepsilon_{t-1}|+\beta\sigma_{t-1}$ | Absolute-value (SD) dynamics | Taylor's book is cited in its 2nd edition (World Scientific 2008; 1st ed. Wiley 1986 has no registry record — see "Unverified"); Schwert (1989) uses absolute residuals from an AR; variance forecast $E[\sigma_{t+k}^2]\ne (E\sigma_{t+k})^2$ | rugarch (`fGARCH`, `AVGARCH`) |48| `higgins1992class` | NARCH (Higgins–Bera): power transform of ARCH | Box–Cox-type nonlinearity in ARCH | Package "NGARCH" names are ambiguous: rugarch `fGARCH(NGARCH)` is the Higgins–Bera power form; `NAGARCH` is the Engle–Ng shift form | rugarch (`fGARCH`, `NGARCH`) |49| `engle1993measuring` | NAGARCH (Engle–Ng): $h_t=\omega+\alpha(\varepsilon_{t-1}-\theta\sigma_{t-1})^2+\beta h_{t-1}$; news-impact curve; sign/size bias tests | Diagnostics for asymmetry; the nonlinear-asymmetric GARCH | Persistence $\alpha(1+\theta^2)+\beta$; sign-bias tests feed the diagnostics block | rugarch (`fGARCH`, `NAGARCH`); tests: custom |50| `sentana1995quadratic` | QGARCH: $h_t=\omega+\alpha\varepsilon_{t-1}^2+\psi\varepsilon_{t-1}+\beta h_{t-1}$ | Quadratic form in lagged shocks; linear asymmetry term | Positivity requires $\psi^2\le4\omega\alpha$-type restrictions; not in arch/rugarch | custom (if time permits) or out of scope |51| `pagan1990alternative` | Early comparison of parametric/nonparametric volatility models | Precedent for model comparison | — | context |5253### a.3 Fractional persistence5455| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |56|---|---|---|---|---|57| `baillie1996fractionally` | FIGARCH(p,d,q): $\phi(L)(1-L)^d\varepsilon_t^2=\omega+[1-\beta(L)]v_t$ | Hyperbolic decay of shocks to variance | Infinite ARCH($\infty$) representation truncated (1000 lags typical); **not** covariance stationary for any $d>0$ (unconditional variance infinite) but strictly stationary; sufficient positivity conditions of BBM are not necessary — use `conrad2006inequality`; $\omega$ small and poorly identified | arch (`FIGARCH`, truncation `truncation`), rugarch (`fiGARCH`) |58| `bollerslev1996modeling` | FIEGARCH | Fractional integration in log variance; stationary for $d<1/2$ | Multi-step variance forecast requires simulation; not in arch; rugarch has no FIEGARCH | custom (phase 3, optional) |59| `tse1998conditional` | FIAPARCH | Fractional + power + asymmetry | Combines FIGARCH truncation with APARCH power; heavy to estimate; not in arch/rugarch | custom (optional) or out of scope |60| `davidson2004moment` | HYGARCH: hyperbolic GARCH | Nests GARCH and FIGARCH with an amplitude parameter | Positivity constraints non-trivial (see Conrad 2007 SSRN, not cited); not in arch/rugarch | custom (optional) or out of scope |61| `conrad2006inequality` | Necessary and sufficient positivity conditions for FIGARCH | Admissibility rules for the FIGARCH block | Replaces BBM sufficient conditions | admissibility checks (custom) |62| `ding1996modeling` | Long-memory volatility via aggregation | Motivation for hyperbolic decay | — | context |63| `chung1999estimating` | FIGARCH re-parameterisation (Chung) | Alternative intercept treatment | **UNVERIFIED** (no registry record found) — not cited | — |6465### a.4 Components, regimes, smooth transition, mixed frequency6667| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |68|---|---|---|---|---|69| `engle1999long` | Component GARCH (long-run/short-run) | Permanent–transitory decomposition of $h_t$ | Chapter title is "A Long-Run and Short-Run Component Model…" (the 1993 UCSD WP was "A permanent and transitory component model…"); rugarch `csGARCH` uses the Engle–Lee parameterisation; Crossref metadata for this chapter has typos corrected in the script from the OUP page | rugarch (`csGARCH`) |70| `engle2008spline` | Spline-GARCH | Deterministic low-frequency component | Needs a trend spline; not a forecasting model per se | out of scope |71| `hamilton1989new` | Markov-switching (filter) | Regime inference | — | regime block reference |72| `hamilton1994autoregressive`, `cai1994markov` | SWARCH / MS-ARCH | First regime-switching ARCH (ARCH only, to avoid path dependence) | Path dependence of GARCH under switching is the key obstacle | context |73| `gray1996modeling`, `klaassen2002improving` | MS-GARCH with collapsing (Gray; Klaassen's improved conditioning) | Tractable MS-GARCH via recombination | Gray and Klaassen collapse differently → not the same likelihood; Klaassen's multi-step forecast is analytic | MSGARCH does **not** implement Gray/Klaassen → custom or out of scope |74| `haas2004new` | MS-GARCH (Haas–Mittnik–Paolella): $K$ parallel GARCH processes, regime-specific variances | Analytic likelihood and forecasts; stationarity conditions | This is the definition implemented in `MSGARCH` (`ardia2019markov`); WP46 "MS-GARCH" = HMP form | MSGARCH (R) |75| `bauwens2010theory`, `augustyniak2014maximum` | Theory/ML estimation of path-dependent MS-GARCH | Bayesian/EM approaches | Path-dependent variant; computationally heavy | out of scope |76| `ardia2019markov`, `ardia2016msgarch` | MSGARCH R package (JSS paper + CRAN record) | Software | GARCH, GJR, EGARCH, TGARCH (Zakoïan) components; ML or MCMC | MSGARCH |77| `ardia2018forecasting` | Large-scale MS-GARCH vs single-regime risk forecasting (426 stocks, indices, FX) | Closest large-scale regime benchmark (VaR/ES, density) | Loss = VaR/ES/density, not QLIKE; see §G | benchmark comparator |78| `gonzalezrivera1998smooth` | Smooth-transition GARCH (STGARCH) | Logistic transition between regimes in the ARCH term | Several ST forms (logistic on $\varepsilon_{t-1}$, exponential); not in arch/rugarch | custom (optional) |79| `hagerud1997smooth` | Smooth-transition ARCH (SSE/EFI WP 162) | Early ST-ARCH | Manual-URL entry (RePEc); title "A Smooth Transition ARCH Model for Asset Returns" | context |80| `engle2013stock` | GARCH-MIDAS | Long-run component driven by low-frequency (macro/realized) variables | Requires an explanatory low-frequency series; WP46 would only use realized-variance MIDAS (Tier B) if at all | arch (`MIDASHyperbolic` is MIDAS-weighted ARCH, **not** GARCH-MIDAS) → custom; conditional on data |81| `ghysels2006predicting`, `ghysels2007midas` | MIDAS regressions for volatility | Mixed-frequency weighting | MIDAS-RV is a regression (non-GARCH comparator) | extension (Tier B) |82| `engle2011forecasting` | Multiplicative component GARCH for intraday volatility | Intraday periodicity | JFEC 9(1), 2011 (Crossref `issued` 2011) — not 2012 | out of scope (daily targets) |8384### a.5 Score-driven and stochastic volatility (adjacent comparators)8586| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |87|---|---|---|---|---|88| `creal2013generalized` | GAS / score-driven models | Update driven by scaled score of the conditional density | GAS with Gaussian density = GARCH; with Student-t density = Beta-t-GARCH (robust to outliers) | GAS R package (`ardia2019generalized`) or custom; labelled **non-GARCH adjacent** |89| `harvey2013dynamic`, `harvey2008beta`, `harvey2014egarch` | Beta-t-EGARCH (DCS) | Log-variance driven by the t-score; closed-form moments | Identical to GAS-t-EGARCH up to scaling; `harvey2008beta` is a Cambridge WP (manual-URL); `harvey2014egarch` adds skewness/leverage | custom (optional) |90| `blasques2015information` | Information-theoretic optimality of score updates | Justification for GAS | — | context |91| `taylor1994modeling`, `kim1998stochastic`, `jacquier1994bayesian`, `harvey1994multivariate` | Stochastic volatility (log-SV) | Latent-variance alternative; KSC's comparison with ARCH | Estimation by MCMC/QML; forecasts require filtering → compute cost class "simulation/Bayesian" (brief) | extension (optional, "if feasible") |92| `taylor2008modelling` | Taylor's book (2nd ed.) | Origin of SV and AVGARCH ideas (1st ed. 1986) | see Unverified note on the 1986 edition | context |9394### a.6 Innovation distributions9596| bibkey | Distribution | Caveats | Planned scope |97|---|---|---|---|98| `bollerslev1987conditionally` | Standardised Student-t ($\nu>2$, unit variance) | Must be the **unit-variance** standardisation; $\nu\le4$ breaks the fourth moment (affects QMLE SEs and some tests) | arch (`StudentsT`), rugarch (`std`) |99| `nelson1991conditional` | GED | Shape $\nu$; $E|z|$ enters EGARCH intercept | arch (`GeneralizedError`), rugarch (`ged`) |100| `hansen1994autoregressive` | Hansen skew-t (autoregressive conditional density) | Skew parameter $\lambda\in(-1,1)$, mode/mean shift; **different parameterisation from Fernández–Steel** | arch (`SkewStudent` = Hansen) |101| `fernandez1998bayesian` | Fernández–Steel skewing ($\xi>0$ inverse-scale) | rugarch `sstd`/`sged` use Fernández–Steel (with mean/variance re-centring); not Hansen | rugarch (`sstd`, `sged`) |102| `bollerslev1992quasi` | Gaussian QMLE robust SEs | Correct inference when the true law is non-Gaussian | all |103104### a.7 QMLE theory, stationarity, moments, constraints105106| bibkey | Result | Use in WP46 |107|---|---|---|108| `bollerslev1992quasi` | QMLE consistency/robust (sandwich) covariance for dynamic models | standard errors |109| `lee1994asymptotic` | GARCH(1,1) QMLE asymptotics incl. IGARCH | inference |110| `lumsdaine1996consistency` | Consistency/normality in IGARCH(1,1) and stationary GARCH(1,1) | inference under near-unit persistence |111| `jensen2004asymptotic` | QMLE normality for nonstationary ARCH | boundary cases |112| `francq2004maximum` | ML estimation of pure GARCH and ARMA-GARCH (general $p,q$) | reference regularity conditions |113| `straumann2006quasi` | Stochastic recurrence equation approach (EGARCH, AGARCH) | EGARCH inference |114| `nelson1990stationarity` | Strict stationarity $E\log(\alpha z^2+\beta)<0$ for GARCH(1,1) | admissibility (strict vs second-order) |115| `bougerol1992stationarity` | Strict stationarity of GARCH(p,q) via top Lyapunov exponent | admissibility |116| `he1999properties`, `ling2002stationarity`, `ling2002necessary` | Moment existence for GARCH/APARCH families | fourth-moment screening, APARCH admissibility |117| `nelson1992inequality` | Necessary and sufficient positivity constraints for GARCH(p,q) | admissibility for (2,1)/(1,2) orders |118| `conrad2006inequality` | FIGARCH positivity | admissibility |119| `lundbergh2002evaluating` | Misspecification tests for GARCH | diagnostics |120121---122123## (b) Realized measures and realized-measure models124125| bibkey | Measure / model | Contribution | Exact-definition caveats | Planned scope |126|---|---|---|---|---|127| `andersen1998answering` | RV as a proxy makes GARCH look good ($R^2$ of MZ regressions) | Founding argument for RV-based evaluation | Uses 5-min FX RV | evaluation design |128| `andersen2001distribution`, `andersen2001distributionstock` | Distribution of realized FX / stock volatility | Log-RV ≈ Gaussian, long memory | JASA 2001 / JFE 2001 (JFE Crossref record lists only the first author; completed in script) | proxy construction |129| `andersen2003modeling` | RV theory + ARFIMA forecasting | RV as consistent estimator of integrated variance | — | reference |130| `barndorff2002econometric` | Asymptotics of RV | Measurement error distribution | — | reference |131| `barndorff2004power` | Bipower variation (jump-robust) | BPV $=\frac{\pi}{2}\sum|r_j||r_{j-1}|$ | Author list completed (Crossref lists one author) | highfrequency (`rBPCov`) / custom |132| `barndorff2008designing`, `barndorff2009realized` | Realized kernels | Noise-robust RV | Needs tick/quote data; with 1-min bars kernels are optional | optional (Tier B sensitivity) |133| `barndorff2010measuring` | Realized semivariance (RS⁺/RS⁻) | Signed variation | book chapter (OUP) | custom |134| `hansen2006realized` | RV and microstructure noise; signature plots | Sampling frequency choice | — | proxy sensitivity (1-min vs 5-min) |135| `hansen2005realized` | Whole-day RV with optimal overnight weighting | **Overnight scaling**: $RV^{day}=\omega_1 r_{on}^2+\omega_2 RV^{open}$ with MSE-optimal weights | JFEC 3(4) 2005; author list completed in script. WP46 must choose and pre-register the overnight treatment (brief: treat overnight separately) | custom (pre-registered) |136| `hansen2006consistent` | Consistent ranking requires robust losses | Precursor of Patton (2011) | — | evaluation design |137| `zhang2005tale`, `aitsahalia2005how`, `jacod2009microstructure` | TSRV, optimal sampling, pre-averaging | Noise-robust estimators | Require higher than 1-min frequency to matter | optional sensitivity |138| `liu2015does` | "Does anything beat 5-minute RV?" (400 estimators, 31 assets) | 5-min RV hard to beat; uses QLIKE + MCS | Template for cross-asset evaluation of estimators | proxy choice (5-min RV primary) |139| `andersen2005correcting`, `andersen2011realized` | Forecast evaluation with RV proxies; noise effects | Corrections for proxy error | — | evaluation |140| `patton2009optimal` | Optimal combinations of RV estimators | — | — | optional |141| `andersen2010parametric` | Parametric vs nonparametric volatility measurement | Survey | — | reference |142| `andersen1999forecasting` | Sampling frequency vs forecast horizon | Multi-horizon variance targets | Horizon-matching rationale | design |143| `corsi2009simple` | HAR-RV: $RV_{t+1}=\beta_0+\beta_d RV_t+\beta_w RV_t^{(5)}+\beta_m RV_t^{(22)}$ | Simple, strong realized benchmark | OLS; log-HAR variant; direct multi-step vs iterated must be stated | highfrequency (`HARmodel`) / custom OLS; **non-GARCH comparator** |144| `andersen2007roughing` | HAR-CJ (continuous/jump split) | Jumps in HAR | needs BPV | optional |145| `patton2015good` | HAR with semivariances (HAR-RS) | Signed jumps | — | optional |146| `bollerslev2016exploiting` | HARQ (measurement-error adjusted) | Time-varying persistence by RQ | needs realized quarticity | optional |147| `clements2021practical`, `branco2024forecasting`, `lyocsa2021stock` | HAR practice; "does anything beat linear models?" (10 indices, 2000–2021); do we need HF data? | Recent HAR-centred benchmarks | see §G | comparators |148| `engle2002new` | New frontiers for ARCH; GARCH-X with realized regressors | GARCH-X concept | Realized regressor enters variance equation additively | arch (`GARCH` + `x` regressors via custom), rugarch (`external.regressors`) |149| `engle2006multiple` | MEM (multiplicative error models) | Joint RV/range dynamics | non-GARCH | out of scope |150| `shephard2010realising` | HEAVY: $h_t=\omega+\alpha RM_{t-1}+\beta h_{t-1}$; $\mu_t=\omega_R+\alpha_R RM_{t-1}+\beta_R\mu_{t-1}$ | Two-equation system; realized measure drives both | Return equation uses lagged RM (no $\varepsilon^2$); closed-form multi-step via the RM equation | highfrequency (`HEAVYmodel`) / custom |151| `hansen2012realized` | Realized GARCH: $\log h_t=\omega+\beta\log h_{t-1}+\gamma\log x_{t-1}$; measurement $\log x_t=\xi+\varphi\log h_t+\tau(z_t)+u_t$ | Joint return/RM model with leverage function | Log-linear vs linear versions; measurement equation is part of the likelihood (not comparable in LL to GARCH); multi-step by the VAR-type recursion | rugarch (`realGARCH`) |152| `hansen2016exponential` | Realized EGARCH | Log-variance with leverage and multiple RMs | JBES 34(2) 2016 | custom |153| `noureldin2012multivariate`, `hansen2014realized`, `bollerslev2018modeling`, `archakov2026multivariate` | Multivariate HEAVY, Realized Beta GARCH, HARQ-covariances, multivariate Realized GARCH (JoE 2026) | Realized-measure multivariate models | Tier C would need realized covariances from synchronised intraday data | out of scope (documented as future work) unless Tier C data permit |154| `fleming2003economic` | Economic value of volatility timing with RV | Economic loss motivation | — | context (secondary) |155| `boudt2012highfrequency` | `highfrequency` R package (CRAN) | RV, BPV, kernels, HAR, HEAVY | version to be pinned | software |156157---158159## (c) Multivariate160161| bibkey | Model | Contribution | Exact-definition caveats | Planned scope |162|---|---|---|---|---|163| `bollerslev1990modelling` | CCC-GARCH | Constant correlation, univariate GARCH margins | PD guaranteed if $R$ PD | rmgarch / custom |164| `engle1995multivariate` | BEKK | PD by construction; quadratic form | Parameter count $O(N^2)$; scalar/diagonal BEKK for $N>3$ | custom (scalar/diagonal BEKK) |165| `engle2002dynamic`, `engle2001theoretical` | DCC(1,1), two-step estimation | Scalable time-varying correlations | $Q_t$ recursion uses $\bar Q$ (unconditional of standardised residuals); **DCC estimator is not consistent** in general — see `aielli2013dynamic` (cDCC); NBER WP 8554 is the theoretical companion | rmgarch (`dccspec`) |166| `tse2002multivariate` | VC-GARCH (Tse–Tsui) | Alternative correlation dynamics | — | out of scope |167| `cappiello2006asymmetric` | Asymmetric DCC (aDCC) | Correlation asymmetry to joint negative shocks | — | rmgarch (`aDCC`) |168| `aielli2013dynamic` | cDCC (corrected DCC) | Consistent DCC estimation | rmgarch implements cDCC; WP46 reports which | rmgarch |169| `vanderweide2002gogarch` | GO-GARCH | Orthogonal factors with univariate GARCH | Identification via ICA/ML; rmgarch `gogarch` | rmgarch |170| `engle2019large` | DCC-NL (nonlinear shrinkage) | Large-$N$ DCC | For $N\le 10$ baskets not needed | out of scope |171| `pakel2021fitting` | Composite likelihood for vast DCC | — | — | out of scope |172| `creal2011dynamic` | Multivariate GAS-t | Score-driven covariance | adjacent | out of scope |173| `bauwens2006multivariate`, `silvennoinen2009multivariate` | Surveys | Taxonomy of MGARCH | — | taxonomy |174| `laurent2012forecasting`, `laurent2013loss` | Forecasting accuracy of 125 MGARCH models with MCS; consistent multivariate loss functions | Define which matrix losses are robust to proxy noise (Frobenius, Stein/QLIKE-matrix) | WP46 Tier C losses must be from the consistent class | evaluation (Tier C) |175| `patton2009evaluating` | Evaluating volatility and correlation forecasts (handbook chapter) | Multivariate MZ and loss definitions | — | evaluation |176| `engle2006testing` | Economic value of correlation forecasts (portfolio variance) | Portfolio-based Tier C diagnostic | — | optional |177| `caporin2014robust` | Robust ranking of MGARCH by dimension | — | — | context |178| `galanos2013rmgarch` | rmgarch (CRAN) | DCC/aDCC/cDCC/GO-GARCH/copula | pin version | software |179180---181182## (d) Forecast evaluation and inference183184| bibkey | Method | Contribution | Exact-definition caveats | Planned scope |185|---|---|---|---|---|186| `patton2011volatility` | Robust loss functions (MSE and QLIKE family) under imperfect proxies | **Primary loss justification**: QLIKE ranking consistent with a conditionally unbiased proxy | Patton's QLIKE $= \log h + y/h$; WP46 uses $y/h-\log(y/h)-1$ (same ranking, zero at $y=h$); proxy must be conditionally unbiased for the *target* (overnight treatment matters) | core |187| `hansen2006consistent` | Consistent ranking | Precursor | — | core |188| `hansen2005forecast` | 330 ARCH-type models, DM/$ and IBM, SPA test | **Closest predecessor** (see §G) | Uses RV proxies, 1-day horizon only | comparator |189| `hansen2003choosing` | Early MCS application to volatility models | — | — | context |190| `diebold1995comparing`, `diebold2015comparing` | DM test; retrospective on use/abuse | Pairwise comparison of loss differentials | For nested models and estimated parameters the DM null is about the *forecasts*, not the models (`diebold2015comparing`) | core |191| `harvey1997testing` | HLN small-sample correction for DM; multi-step $h$ | Use with HAC lag $h-1$ at horizon $h$ | WP46 horizon 22 → overlapping targets | core |192| `west1996asymptotic`, `clark2007approximately`, `giacomini2006tests` | Parameter-estimation uncertainty; nested-model tests; conditional predictive ability (rolling windows) | GW framework fits rolling re-estimation | GW requires finite rolling windows (not expanding) for asymptotics | inference design |193| `white2000reality`, `hansen2005test` | Reality check; SPA test | Multiple-comparison control vs a benchmark | SPA uses studentised statistics and a consistent p-value; both need stationary bootstrap | core (SPA vs GARCH(1,1)) |194| `hansen2011model` | Model Confidence Set | Set of models not significantly dominated at level $\alpha$ | $T_{max}$ vs $T_R$ statistics; block bootstrap parameters must be pre-registered | core |195| `romano2005stepwise` | StepM multiple testing | FWER control | alternative to SPA | optional |196| `holm1979simple` | Holm step-down | Simple FWER control for pairwise tables | OpenAlex record (Crossref returns 404 for the JSTOR DOI) | optional |197| `politis1994stationary`, `politis2004automatic` | Stationary bootstrap; automatic block length | Bootstrap for SPA/MCS | Patton–Politis–White 2009 correction exists (not cited; see note) | core |198| `newey1987simple`, `newey1994automatic` | HAC covariance; automatic lag | DM variance at $h>1$ | — | core |199| `mincer1969evaluation` | MZ regression $y=a+b\hat h+e$ | Calibration/unbiasedness check | NBER chapter (manual-URL) | secondary |200| `andersen1998answering`, `andersen2005correcting` | RV-based $R^2$ and corrections | — | — | secondary |201| `poon2003forecasting` | Survey of 93 volatility forecasting papers | Historical meta-view | — | related literature |202| `awartani2005predicting` | S&P 500 GARCH comparison (asymmetries) | Early benchmark | — | comparator |203| `brownlees2011practical` | Calm and storm: many assets, QLIKE, 1-day to multi-step, 2008 crisis | **Closest cross-asset regime benchmark** (see §G) | Journal of Risk 14(2), 2011 | comparator |204| `bollerslev2018risk` | Risk everywhere (RFS 2018, **not** JFE) | Cross-asset realized-volatility modelling (50+ futures), HAR-type | — | comparator |205| `patton2020comparing` | Comparing possibly misspecified forecasts (JBES 2020) | Loss choice matters under misspecification | Reinforces reporting several losses | design |206| `gneiting2011making`, `gneiting2007strictly` | Consistent scoring functions; proper scoring rules | Loss/functional consistency | QLIKE is consistent for the conditional variance (Bregman class) | design |207| `amisano2007comparing`, `diks2011likelihood` | Weighted likelihood-ratio / tail-weighted density tests | Log-score comparisons when a density is supplied | — | secondary (log score) |208| `lopez2001evaluating` | Evaluating volatility models (probability-based losses) | — | — | context |209| `hansen2015equivalence` | OOS comparisons ≡ Wald statistics | Caution on nested OOS tests | — | context |210| `christoffersen2000how` | Relevance of volatility forecasting for risk management decays with horizon | Horizon 22 relevance | — | context |211| `kourtis2016international` | Implied vs realized vs GARCH across 13 indices | HAR best at daily horizon | — | comparator |212213---214215## (e) Tail risk216217| bibkey | Method | Contribution | Caveats | Planned scope |218|---|---|---|---|---|219| `kupiec1995techniques` | Unconditional coverage (POF) test | VaR hit frequency | low power at 1% with short samples | core |220| `christoffersen1998evaluating` | Conditional coverage / independence (Markov) tests | Clustering of hits | — | core |221| `christoffersen2004backtesting` | Duration-based backtest | Alternative independence test | author list completed in script | optional |222| `engle2004caviar` | CAViaR + dynamic quantile (DQ) test | DQ regression test for hits | DQ test used as the conditional test in WP46 | core (DQ test); CAViaR as comparator = extension |223| `berkowitz2011evaluating` | Evaluation of VaR with desk-level data; CAViaR-type tests compared | Power comparison of backtests | — | design |224| `fissler2016higher`, `fissler2015expected` | Joint elicitability of (VaR, ES); FZ loss | Joint scoring $S_{FZ}$ | arXiv v1 2015 (bibkey year follows the fetched record); Risk magazine version 2016 | core (FZ0 loss) |225| `patton2019dynamic` | Dynamic semiparametric ES models; FZ0 loss | ES forecast evaluation | — | core (loss definition) |226| `nolde2017elicitability` | Elicitability and backtesting (comparative vs traditional backtests) | Framework | — | design |227| `acerbi2014backtesting` | ES backtests (Z1–Z3) | Direct ES backtests | OpenAlex-only record; Risk.net page blocked for automated fetch (search snippet confirmed authors/title); title stored as fetched | optional |228| `bayer2022regression`, `dimitriadis2019joint`, `bayer2020esback` | Regression-based ES backtests; joint quantile/ES regression; `esback` | ESR backtests | JFEC 20(3) 2022 | core (ESR test via R `esback`) |229| `taylor2019forecasting` | AL-based joint VaR/ES score | AL log-score as alternative joint loss | JBES 37(1) 2019 | secondary |230| `ziegel2016coherence` | ES not elicitable alone | Why joint scores are needed | Math. Finance 26(4) 2016 | context |231| `mcneil2000estimation` | GARCH-EVT | Semi-parametric tails | extension comparator | optional |232| `kuester2006value` | VaR prediction: comparison of strategies (NASDAQ) | Early tail benchmark; GARCH-EVT/skew-t favoured | JFEC 4(1) 2006 | comparator |233| `giot2003value` | VaR for long/short positions with skewed-t APARCH | Skewed-t relevance for tails | — | comparator |234235---236237## (f) Large-scale benchmarks, ML extensions, software238239| bibkey | Study | Design | Relation to WP46 |240|---|---|---|---|241| `hansen2005forecast` | 330 models, DM/\$ (1987–1993) and IBM (1990–1999), 1-day, RV proxies, SPA | GARCH(1,1) not beaten on FX; beaten by leverage models on IBM | direct predecessor |242| `marcucci2005forecasting` | MS-GARCH vs GARCH on S&P 100, 1-, 5-, 10-, 22-day, several losses, SPA | Regime models win short horizons only | predecessor (horizons) |243| `andersen2006volatility` | Handbook chapter: volatility and correlation forecasting | Survey of methods | related literature |244| `brownlees2011practical` | Many US assets, GARCH family, QLIKE, multi-step, crisis vs calm | Asymmetric GARCH best overall; calm/storm split | predecessor (regimes) |245| `ardia2018forecasting` | 426 assets, MS-GARCH vs single regime, VaR/ES/density, 2005–2016 | MS helps for tails/density | predecessor (regimes, tails) |246| `kuester2006value` | VaR strategies on NASDAQ | tails | predecessor (tails) |247| `liu2015does` | 400 RV estimators, 31 assets, QLIKE, MCS | template for proxy choice | predecessor (Tier B proxies) |248| `laurent2012forecasting` | 125 MGARCH, MCS, robust matrix losses | Tier C template | predecessor (Tier C) |249| `lyocsa2021stock` | HF vs daily information for stock-index volatility | information-set comparison | predecessor (Tier A vs B) |250| `kourtis2016international` | 13 indices, implied/RV/GARCH | HAR dominant daily | predecessor |251| `christensen2023machine` | ML (trees/NN) vs HAR with many predictors, US equities (JFEC 21(5) 2023) | ML gains with external predictors | ML extension comparator |252| `bucci2020realized` | Neural networks for RV (JFEC 2020) | — | ML extension |253| `zhang2024volatility` | Zhang, Zhang, Cucuringu & Qian (JFEC 22(2) 2024): ML + intraday commonality, US stocks | note: the brief's "Zhang, Zohren et al." is a misattribution; Zohren co-authors `rahimikia2021realised` | ML extension comparator |254| `rahimikia2024machine`, `rahimikia2021realised` | ML for RV forecasting (SSRN 2024; arXiv 2021 word-embedding) | working papers (labelled) | ML extension |255| `branco2024forecasting` | 10 indices 2000–2021, linear vs nonlinear ML vs HAR (JEF 2024) | "nothing beats linear models" | 2024 benchmark comparator |256| `gunnarsson2024prediction` | Review of AI/ML RV and IV prediction (IRFA 2024) | survey of the ML strand | related literature |257| `brini2026forecasting` | arXiv 2607.05291 (July 2026): 9 zero-shot foundation models vs 8 econometric specs, 50 assets (equities, FX, futures), h = 1/5/22, QLIKE, MCS, DM with BH correction | **closest 2026 cross-asset benchmark**, realized-measure only, no GARCH tier, no failure/compute accounting; preprint | 2026 benchmark comparator |258| `brini2024comparison` | arXiv 2404.04962: crypto vs mature asset classes volatility | crypto context | context |259| `reisenhofer2022harnet` | HARNet (arXiv 2022) | CNN extension of HAR | ML extension |260| `kim2018forecasting` | LSTM + GARCH hybrids (ESWA 2018) | hybrid strand | ML extension context |261| `catania2019forecasting`, `ardia2019regime`, `trucios2019forecasting` | Crypto volatility/risk forecasting (GARCH/MS-GARCH, robust) | crypto block references | design (crypto instruments) |262| `sheppard2025arch` | `arch` v8.0.0, Zenodo DOI 10.5281/zenodo.17404619 (21 Oct 2025; concept DOI 10.5281/zenodo.593254) | Python reference library | software (pinned 8.0.0) |263| `galanos2011rugarch`, `galanos2013rmgarch` | rugarch / rmgarch CRAN records (DOIs registered by CRAN; `issued` = first release) | R reference libraries (1.5-6) | software |264| `ardia2019markov`, `ardia2016msgarch` | MSGARCH JSS + CRAN | — | software |265| `ardia2019generalized` | GAS package JSS | — | software (optional) |266| `boudt2012highfrequency` | highfrequency CRAN | — | software |267| `catania2014mcs` | MCS R package (CRAN) | MCS implementation cross-check | software (optional; WP46 implements MCS in Python and cross-checks) |268| `bayer2020esback` | esback CRAN | ES backtests | software |269270---271272## Definition caveats that WP46 must not blur (C1)2732741. **TGARCH ≠ GJR.** Zakoïan (1994) models $\sigma_t$ with separate slopes on $\varepsilon^+$ and $\varepsilon^-$ (power 1); GJR (1993) models $h_t$ with an indicator on negative shocks (power 2). rugarch `fGARCH/TGARCH` = Zakoïan; EViews "TARCH", many textbooks and some Python code = GJR. `arch` has no Zakoïan TGARCH (its `GARCH(p,o,q)` is GJR; its `APARCH` with $\delta=1$ reproduces Zakoïan). WP46 names: `gjr` and `tgarch_zakoian`.2752. **EGARCH parameterisations** differ across Nelson (1991), `arch` and rugarch (ordering/labels of the sign and magnitude coefficients, and the $E|z|$ constant depends on the innovation law). Model cards map parameters explicitly; cross-checks compare log-likelihoods, not raw coefficients.2763. **NGARCH vs NAGARCH.** Higgins–Bera (1992) is a power/Box–Cox nonlinearity; Engle–Ng (1993) NAGARCH shifts the news-impact curve. rugarch `fGARCH` has both as distinct submodels.2774. **Persistence/stationarity conditions are family-specific** (brief): $\alpha+\beta<1$ (GARCH, second-order), $\alpha+\beta+\gamma/2<1$ (GJR, symmetric $z$), $|\beta|<1$ (EGARCH), $E\log(\alpha z^2+\beta)<0$ (strict, GARCH(1,1), `nelson1990stationarity`), Lyapunov condition for $(p,q)$ (`bougerol1992stationarity`), APARCH moment conditions (`ling2002necessary`), FIGARCH strictly but not covariance stationary, positivity via `nelson1992inequality` / `conrad2006inequality`.2785. **Component GARCH** has two common parameterisations (Engle–Lee permanent/transitory vs the equivalent rugarch `csGARCH`); forecasts coincide but constraints are written differently.2796. **MS-GARCH** = Haas–Mittnik–Paolella (2004) parallel-process form (as in `MSGARCH`), not Gray (1996) or Klaassen (2002) collapsing forms, and not the path-dependent model of `bauwens2010theory`.2807. **Realized GARCH** includes a measurement equation in the likelihood → in-sample likelihoods are not comparable with GARCH; log-linear version is the default (`hansen2012realized`). **HEAVY** uses the lagged realized measure (not $\varepsilon^2$) in the return-variance equation.2818. **DCC vs cDCC** (`aielli2013dynamic`): rmgarch estimates cDCC by default; report which.2829. **Skewed Student-t** means Hansen (1994) in `arch` and Fernández–Steel (1998) in rugarch; densities and skewness parameters are not interchangeable (brief: "reconcile probability density conventions").28310. **QLIKE** is reported as $y/h-\log(y/h)-1$ (zero at $y=h$); Patton's $\log h+y/h$ differs by a term in $y$ only → identical rankings (brief).28411. **Overnight variance.** Tier B targets must say whether the proxy is open-to-close RV, RV + overnight squared return, or the optimally weighted whole-day RV (`hansen2005realized`); GARCH forecasts are close-to-close.28512. **RiskMetrics** $\lambda=0.94$ (1996) vs RM2006 multi-scale kernel (`zumbach2009riskmetrics`) are different baselines.28613. **DM at $h>1$** uses HAC with $h-1$ lags and the HLN correction; MCS/SPA bootstrap block length is pre-registered (Politis–White automatic selection as default, documented).28714. **Joint VaR–ES evaluation** uses the FZ0 loss (`patton2019dynamic`, `fissler2015expected`); unconditional/conditional coverage and DQ tests are reported for VaR; ESR backtests (`bayer2022regression`) for ES.288289---290291## G. Closest large-scale benchmarks and incremental contribution292293| Study | Assets / period | Models | Horizons | Losses / inference | Tiers | Failure & compute accounting | Pre-registration |294|---|---|---|---|---|---|---|---|295| `hansen2005forecast` | DM/\$ 1987–1993; IBM 1990–1999 (2 series) | 330 ARCH-type (orders × distributions × asymmetries) | 1 day | MSE, QLIKE etc. with RV proxy; SPA/RC | daily only | none | none |296| `marcucci2005forecasting` | S&P 100 (1 series) | MS-GARCH vs GARCH/EGARCH/GJR | 1, 5, 10, 22 | several losses, SPA | daily | none | none |297| `brownlees2011practical` | US equity index, sector ETFs, stocks (≈ a dozen+ series), 2000–2008 crisis | GARCH, GJR/TARCH, EGARCH, APARCH, NGARCH; estimation window/frequency variants | 1 to multi-step | QLIKE, DM; calm/storm | daily | window/frequency variants; no failure accounting | none |298| `ardia2018forecasting` | 426 stocks/indices/FX, 2005–2016 | MS-GARCH vs single-regime | 1 | VaR/ES/density scores, MCS | daily | none | none |299| `kuester2006value` | NASDAQ (1 series) | GARCH-type, EVT, CAViaR, skew-t | 1 | VaR backtests | daily | none | none |300| `liu2015does` | 31 assets (ETFs, stocks, FX, futures) | 400 RV *estimators* | — | QLIKE, MCS | realized | none | none |301| `laurent2012forecasting` | 10 US stocks | 125 MGARCH | 1 | consistent matrix losses, MCS | multivariate | none | none |302| `lyocsa2021stock` | stock indices | HAR vs GARCH-type | 1–22 | QLIKE/MSE, MCS | daily vs HF | none | none |303| `christensen2023machine` | US stocks (RV) + predictors | ML vs HAR | 1, 5, 22 | MSE/QLIKE, DM/MCS | realized | none | none |304| `zhang2024volatility` | US stocks (RV, intraday commonality) | ML vs HAR/OLS | 1 (+) | MSE/QLIKE, MCS | realized | none | none |305| `branco2024forecasting` | 10 indices, 2000–2021 | linear vs ML vs HAR | 1, 5, 22 | losses, MCS, econ. value | realized | none | none |306| `brini2026forecasting` (arXiv) | 50 assets (equities, FX, futures) | 9 foundation models vs 8 econometric (HAR family etc.) | 1, 5, 22 | QLIKE, MCS, DM+BH | realized | none | none |307| **WP46 (planned)** | ≈ 20–40 instruments across ETFs, large-cap stocks, Treasury/energy/metal futures, FX, BTC/ETH (subject to FinData coverage), 2000–2026 | full canonical GARCH taxonomy (classical, asymmetric/power, fractional, component/regime, GARCH-X), realized-measure models (Realized GARCH, HEAVY, HAR), multivariate (CCC/DCC/aDCC/BEKK/GO), adjacent comparators (GAS, SV if feasible), explicitly labelled ML extension | 1, 5, 22 (same-horizon proxies) | QLIKE primary; MSE/MAE/log score secondary; DM-HLN, SPA, MCS with pre-registered bootstrap; VaR/ES (UC/CC/DQ, FZ0, ESR); regime splits pre-defined | A (daily), B (realized), C (multivariate), separately scored | median/total CPU time, peak RSS, iterations, convergence failures, inadmissible estimates, forecast coverage; common-success vs failure-adjusted samples; Pareto frontier | frozen protocol before any test loss is seen (git tag) |308309**What is new (relative to the table).**3101. **Breadth × tiers in one design.** No listed study combines a near-complete *GARCH* taxonomy with realized-measure and multivariate tiers on the same cross-asset universe (ETFs, stocks, futures, FX, crypto) over 2000–2026 with identical rolling origins per tier. Hansen–Lunde (2005) has breadth of specifications but two series and one horizon; the realized-measure benchmarks (`liu2015does`, `christensen2023machine`, `zhang2024volatility`, `branco2024forecasting`, `brini2026forecasting`) have breadth of assets but exclude the GARCH tier or treat it as a single baseline.3112. **Failure and compute accounting as outcomes.** None of the comparators reports convergence failures, inadmissible estimates, CPU/memory cost or a failure-adjusted ranking; WP46 treats them as first-class results (C3), which is where the "is any gain worth the cost" question lives.3123. **Pre-registration and multiplicity discipline.** None of the comparators pre-registers the universe, losses, bootstrap settings and regime definitions; WP46 freezes them before test losses are inspected and reports MCS/SPA with dependence across assets discussed.3134. **Definition-faithful taxonomy (C1)** with per-architecture model cards and cross-package likelihood checks; the comparators rely on one package's naming.3145. **Cross-tier reconciliation.** Explicit information-set accounting (Tier A vs B) with a matched-information variant, instead of pooling daily and realized models in one leaderboard.315316**What is not new (and must be said so in the paper).**317- The core question ("does anything beat GARCH(1,1)?") and the SPA/MCS/QLIKE toolkit are Hansen–Lunde (2005), Hansen (2005), Hansen–Lunde–Nason (2011), Patton (2011).318- Asymmetric GARCH beating GARCH(1,1) on equities (Hansen–Lunde 2005 IBM; Brownlees–Engle–Kelly 2011; Awartani–Corradi 2005) and HAR/realized models beating daily models when intraday data exist (Andersen–Bollerslev–Diebold–Labys 2003; Corsi 2009; Lyócsa et al. 2021; Kourtis et al. 2016) are established results; WP46 can at best quantify their stability across assets, horizons and regimes.319- Regime-dependence of model rankings is documented by Marcucci (2005), Brownlees–Engle–Kelly (2011) and Ardia et al. (2018).320- Horizons 1/5/22 and QLIKE-with-MCS are the standard design of the 2023–2026 realized-volatility/ML benchmarks.321- Multivariate loss consistency and MCS for MGARCH are Laurent–Rombouts–Violante (2012, 2013).322- An ML extension would replicate the 2020–2026 strand rather than extend it; it is therefore clearly labelled as an extension and is not part of the GARCH taxonomy claims.323- The 2026 Brini preprint shows that a 50-asset, three-horizon, QLIKE/MCS realized-volatility benchmark already exists; WP46's distinct value there is the GARCH tier, the information-set reconciliation and the operational (failure/compute) dimension — not the realized-volatility leaderboard itself.324325**No 2023–2026 peer-reviewed "does anything beat GARCH(1,1) revisited" study was found** (searches in the log below); the GARCH-tier breadth claim therefore rests on the absence of such a study up to 2026-11-09 and must be re-checked before submission.326327---328329## Search log (all on 2026-11-09)330331| Tool | Query / request | Outcome |332|---|---|---|333| Crossref REST (`/works?query.bibliographic=…`, rows=3, polite UA) | 4 batches, 190 bibliographic queries for every candidate from the brief + extensions (univariate theory; realized + multivariate; evaluation + tail; benchmarks/ML/software) | DOIs discovered/corrected for ~185 items; not found: Hagerud 1997, Chung 1999, Mincer–Zarnowitz 1969, Acerbi–Székely 2014, Fissler–Ziegel–Gneiting 2016 (Risk), Taylor 1986 (1st ed.), RiskMetrics TD, Engle & Lee 1999 (found afterwards via the OUP DOI) |334| Crossref REST (`/works/<doi>`) | direct checks of 16 DOIs (Andersen et al. 2001 ×2, Christoffersen–Diebold 2000, Diebold 2015, SSRN/NBER records, books, OUP chapters, CRAN package DOIs ×7) | all resolved |335| arXiv API (`export.arxiv.org/api/query?id_list=`) | 1507.00244, 2108.00480, 2607.05291, 2205.07719, 2404.04962 | all resolved (first attempt rate-limited; retried with 3 s spacing) |336| OpenAlex API (`/works?search=`, `/works?filter=title.search:`) | Holm 1979; Taylor 1986; RiskMetrics 1996; Acerbi–Székely 2014; Chung 1999 | Holm (W2121044470, DOI 10.2307/4615733), Acerbi–Székely (W2292483766, no venue) found; Taylor 1986 only as the 2007/2008 World Scientific edition and 1987 book reviews; Chung 1999 not found |337| Zenodo API | records/17404619 | arch v8.0.0, 2025-10-21, DOI 10.5281/zenodo.17404619, concept 10.5281/zenodo.593254 |338| WebFetch | OUP chapter 421087965 (Engle–Lee 1999); EconPapers hhs:hastef:0162 (Hagerud); EconPapers cam:camdae:0840 (Harvey–Chakravarty); NBER chapter page (Mincer–Zarnowitz); Wiley page for Taylor 1986 (404); Risk.net Acerbi page (blocked "client challenge"); JSTOR 4615733 (blocked); EconPapers ntu:ntugec:9904 (404) | see Unverified |339| curl | MSCI PDF of the RiskMetrics Technical Document (HTTP 200, application/pdf; cover page read with pdftotext) | confirmed |340| WebSearch | "volatility forecasting benchmark GARCH 2024 'does anything beat' large-scale comparison" | only Hansen–Lunde 2005 + a 2024 HEC Montréal master's thesis |341| WebSearch | "'Forecasting realized volatility: Does anything beat linear models?' Branco Rubesam Zevallos" | JEF 78 (2024), DOI 10.1016/j.jempfin.2024.101524 |342| WebSearch | "model confidence set volatility models 2023 cross-asset GARCH realized GARCH HAR forecast comparison 2025" | Kourtis–Markellos–Symeonidis 2016 (JFM); theses |343| WebSearch | "'realized GARCH' forecast comparison 2024 2025 HAR HEAVY QLIKE model confidence set multiple assets journal" | arXiv 2607.05291 (Brini 2026); arXiv 2609.29515 (network Realized GARCH–Itô, not verified/cited); theses |344| WebSearch | "GARCH(1,1) versus machine learning volatility forecasting large cross-section 2025 …" | working papers/theses only; no journal benchmark |345| WebSearch | "'does anything beat a GARCH' 2023 OR 2024 OR 2025 revisited twenty years later volatility forecast" | nothing after 2005 |346| WebSearch | "Sheppard arch Python package Zenodo DOI bashtage/arch latest release 2025" | Zenodo 17404619 (v8.0.0) |347| WebSearch | "arXiv 2025 2026 'volatility forecasting' benchmark GARCH HAR cross-asset 'foundation models' …" | Brini 2026 (arXiv 2607.05291); VolaTTM write-up (not citable); Research Square preprint rs-10306663 (not verified) |348| WebSearch | Engle & Lee 1999 Festschrift chapter | OUP chapter 20, pp. 475–497, title "A Long-Run and Short-Run Component Model…" |349| WebSearch | Acerbi–Székely 2014 Risk magazine | Risk.net technical paper 2381658 (abstract only) |350| WebSearch | "2025 OR 2026 'volatility forecasting' comparison 'asset classes' ETFs futures FX cryptocurrencies GARCH … MCS QLIKE" | Brini 2026; MDPI/IJFS crypto papers (not verified, not cited); preprints |351352MCP note: the `openalex` and `anthropic` MCP servers failed to connect in this session; OpenAlex was queried through its public REST API with curl instead.353354---355356## Unverified / not found / caveats on verified items357358| Item | Status | Detail |359|---|---|---|360| Chung (1999), "Estimating the fractionally integrated GARCH model", NTU working paper | **UNVERIFIED — not in .bib** | No Crossref, OpenAlex or EconPapers record found (EconPapers `ntu:ntugec:9904` returned 404). The Chung re-parameterisation is mentioned in the matrix text only. |361| Taylor (1986), *Modelling Financial Time Series*, Wiley (1st ed.) | not in .bib as such | Wiley page 404; Google Books API returned nothing; OpenAlex only has the 2007/2008 World Scientific 2nd edition (Crossref DOI 10.1142/6578) and 1987 book reviews. Cited as `taylor2008modelling` with "2nd ed. (1st ed. 1986)". |362| Hagerud (1997) | manual-URL (EconPapers) | Actual title: "A Smooth Transition ARCH Model for Asset Returns" (not "A new non-linear GARCH model"); SSE/EFI WP 162. |363| Harvey & Chakravarty (2008) Beta-t-(E)GARCH | manual-URL (EconPapers) | Cambridge WP 0840; the published successor used is `harvey2014egarch` (CSDA) and the book `harvey2013dynamic`. |364| Mincer & Zarnowitz (1969) | manual-URL (NBER) | Page range not shown on the NBER chapter page → omitted. |365| J.P. Morgan/Reuters (1996) RiskMetrics Technical Document | manual-URL (MSCI PDF) | Cover page read; cited as `@techreport`. |366| Sheppard `arch` | manual (Zenodo API) | DataCite DOI, not Crossref. |367| Holm (1979) | verified via OpenAlex | Crossref returns 404 for DOI 10.2307/4615733 (JSTOR-registered); OpenAlex record carries the DOI, journal, volume 6, pp. 65–70. JSTOR page blocked. |368| Acerbi & Székely (2014) | verified via OpenAlex (weak record) | OpenAlex record has authors/title/year but no venue; Risk.net page blocked for automated fetch; venue field completed as "Risk (Risk.net technical paper)" with the Risk.net URL from search results. Treat as a secondary citation. |369| Fissler, Ziegel & Gneiting | verified via arXiv (2015) | bibkey `fissler2015expected` (arXiv v1, 2015-07-01); the Risk magazine 2016 version has no registry record. |370| Engle & Lee (1999) | verified via Crossref (OUP) | Crossref metadata contains typos ("Cointigration… forecating", "PressOxford", "Gary g. J") corrected in `FIELD_FIX` from the OUP page. |371| Bollerslev, Hood, Huss & Pedersen (2018) | verified | Published in *RFS* 31(7), not JFE as stated in the task list. |372| Brownlees, Engle & Kelly (2011) | verified | *Journal of Risk* 14(2), 2011/12 (not JFEC). |373| Patton (2020) | verified | *JBES* 38(4), 2020 (Crossref `issued` 2019 = online). |374| Engle & Sokalska | verified | *JFEC* 9(1), 2011 (not 2012). |375| "Zhang, Zohren et al. 2024" (task list) | corrected | The JFEC 2024 intraday-commonality paper is Zhang, Zhang, Cucuringu & Qian; Zohren co-authors `rahimikia2021realised` (arXiv). |376| "Lunde & Hansen comparisons" (task list) | interpreted | Covered by `hansen2005forecast`, `hansen2006consistent`, `hansen2005realized`, `hansen2003choosing`. |377| Zumbach RM2006 | verified as SSRN posting (2009) | bibkey year follows the registry record; original RiskMetrics Group document is 2007. |378| Patton, Politis & White (2009) correction to Politis–White | not added | not required for the design; add if the automatic block length is used verbatim. |379| arXiv 2609.29515 (network Realized GARCH–Itô), Research Square rs-10306663, VolaTTM, MDPI/IJFS 2026 crypto papers | not verified, not cited | surfaced by search only. |380| Truncated Crossref author lists completed in `AUTHOR_FIX` | verified DOI/title | `barndorff2004power`, `barndorff2008designing`, `hansen2005realized`, `hansen2011model`, `haas2004new`, `kuester2006value`, `christoffersen2004backtesting`, `conrad2006inequality`, `andersen2001distributionstock`, `bollerslev2010glossary` (and editors of `bauwens2012handbook`). |381| JSS/SNDE articles without page numbers | verified | `ardia2019markov`, `ardia2019generalized`, `gonzalezrivera1998smooth`, `marcucci2005forecasting` use article numbers (Crossref has no `page`). |382