WP46 — Literature matrix (Phase 0)
Status: Phase 0 deliverable (literature inventory). Literature cutoff 2026-11-09. Every bibkey below exists in
paper/references.bib, which is generated by scripts/build_references.py only from records whose title was
verified against Crossref (193), arXiv (5) or OpenAlex (2), plus five items with no registry record that were
confirmed by fetching a publisher/NBER/RePEc/Zenodo/MSCI page (manual (URL fetched)). Per-key evidence (identifier,
fetched title, date, source) is in results/metrics/references_verification.json; the single unverified candidate is in
results/metrics/references_unverified.json and is not cited anywhere.
Counts (run of 2026-11-09): 206 candidates → 205 entries written to the .bib (200 registry-verified: 193 Crossref,
5 arXiv, 2 OpenAlex; + 5 manual-URL), 1 unverified and excluded: chung1999estimating.
Scope column. "Planned scope" is the intended implementation route for WP46 and is not a completion claim; the
binding list is configs/model_registry.yaml once frozen by the pre-registered protocol. Routes: arch (Python arch
8.0.0, sheppard2025arch), rugarch (R 1.5-6, galanos2011rugarch), rmgarch (galanos2013rmgarch), MSGARCH
(ardia2016msgarch), highfrequency (boudt2012highfrequency), custom (own implementation, must pass the
stronger tests of CLAUDE.md rule 6), extension (clearly labelled non-GARCH / ML extension), out of scope.
Conventions: $r_t = \mu_t + \varepsilon_t$, $\varepsilon_t = \sigma_t z_t$, $z_t \sim$ i.i.d. $(0,1)$; $h_t=\sigma_t^2$. Daily log returns are in percent (CLAUDE.md rule 4), so $h_t$ is in percent².
(a) Univariate ARCH/GARCH architectures
a.1 Classical
| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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 |
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) |
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) |
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) |
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 |
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 |
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 |
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 |
a.2 Asymmetric and power
| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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 |
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) |
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) |
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 |
taylor2008modelling, schwert1989why |
AVGARCH / Taylor–Schwert: $\sigma_t=\omega+\alpha | \varepsilon_{t-1} | +\beta\sigma_{t-1}$ | Absolute-value (SD) dynamics |
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) |
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 |
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 |
pagan1990alternative |
Early comparison of parametric/nonparametric volatility models | Precedent for model comparison | — | context |
a.3 Fractional persistence
| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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) |
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) |
tse1998conditional |
FIAPARCH | Fractional + power + asymmetry | Combines FIGARCH truncation with APARCH power; heavy to estimate; not in arch/rugarch | custom (optional) or out of scope |
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 |
conrad2006inequality |
Necessary and sufficient positivity conditions for FIGARCH | Admissibility rules for the FIGARCH block | Replaces BBM sufficient conditions | admissibility checks (custom) |
ding1996modeling |
Long-memory volatility via aggregation | Motivation for hyperbolic decay | — | context |
chung1999estimating |
FIGARCH re-parameterisation (Chung) | Alternative intercept treatment | UNVERIFIED (no registry record found) — not cited | — |
a.4 Components, regimes, smooth transition, mixed frequency
| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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) |
engle2008spline |
Spline-GARCH | Deterministic low-frequency component | Needs a trend spline; not a forecasting model per se | out of scope |
hamilton1989new |
Markov-switching (filter) | Regime inference | — | regime block reference |
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 |
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 |
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) |
bauwens2010theory, augustyniak2014maximum |
Theory/ML estimation of path-dependent MS-GARCH | Bayesian/EM approaches | Path-dependent variant; computationally heavy | out of scope |
ardia2019markov, ardia2016msgarch |
MSGARCH R package (JSS paper + CRAN record) | Software | GARCH, GJR, EGARCH, TGARCH (Zakoïan) components; ML or MCMC | MSGARCH |
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 |
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) |
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 |
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 |
ghysels2006predicting, ghysels2007midas |
MIDAS regressions for volatility | Mixed-frequency weighting | MIDAS-RV is a regression (non-GARCH comparator) | extension (Tier B) |
engle2011forecasting |
Multiplicative component GARCH for intraday volatility | Intraday periodicity | JFEC 9(1), 2011 (Crossref issued 2011) — not 2012 |
out of scope (daily targets) |
a.5 Score-driven and stochastic volatility (adjacent comparators)
| bibkey | Model / method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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 |
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) |
blasques2015information |
Information-theoretic optimality of score updates | Justification for GAS | — | context |
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") |
taylor2008modelling |
Taylor's book (2nd ed.) | Origin of SV and AVGARCH ideas (1st ed. 1986) | see Unverified note on the 1986 edition | context |
a.6 Innovation distributions
| bibkey | Distribution | Caveats | Planned scope |
|---|---|---|---|
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) |
nelson1991conditional |
GED | Shape $\nu$; $E | z |
hansen1994autoregressive |
Hansen skew-t (autoregressive conditional density) | Skew parameter $\lambda\in(-1,1)$, mode/mean shift; different parameterisation from Fernández–Steel | arch (SkewStudent = Hansen) |
fernandez1998bayesian |
Fernández–Steel skewing ($\xi>0$ inverse-scale) | rugarch sstd/sged use Fernández–Steel (with mean/variance re-centring); not Hansen |
rugarch (sstd, sged) |
bollerslev1992quasi |
Gaussian QMLE robust SEs | Correct inference when the true law is non-Gaussian | all |
a.7 QMLE theory, stationarity, moments, constraints
| bibkey | Result | Use in WP46 |
|---|---|---|
bollerslev1992quasi |
QMLE consistency/robust (sandwich) covariance for dynamic models | standard errors |
lee1994asymptotic |
GARCH(1,1) QMLE asymptotics incl. IGARCH | inference |
lumsdaine1996consistency |
Consistency/normality in IGARCH(1,1) and stationary GARCH(1,1) | inference under near-unit persistence |
jensen2004asymptotic |
QMLE normality for nonstationary ARCH | boundary cases |
francq2004maximum |
ML estimation of pure GARCH and ARMA-GARCH (general $p,q$) | reference regularity conditions |
straumann2006quasi |
Stochastic recurrence equation approach (EGARCH, AGARCH) | EGARCH inference |
nelson1990stationarity |
Strict stationarity $E\log(\alpha z^2+\beta)<0$ for GARCH(1,1) | admissibility (strict vs second-order) |
bougerol1992stationarity |
Strict stationarity of GARCH(p,q) via top Lyapunov exponent | admissibility |
he1999properties, ling2002stationarity, ling2002necessary |
Moment existence for GARCH/APARCH families | fourth-moment screening, APARCH admissibility |
nelson1992inequality |
Necessary and sufficient positivity constraints for GARCH(p,q) | admissibility for (2,1)/(1,2) orders |
conrad2006inequality |
FIGARCH positivity | admissibility |
lundbergh2002evaluating |
Misspecification tests for GARCH | diagnostics |
(b) Realized measures and realized-measure models
| bibkey | Measure / model | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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 |
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 |
andersen2003modeling |
RV theory + ARFIMA forecasting | RV as consistent estimator of integrated variance | — | reference |
barndorff2002econometric |
Asymptotics of RV | Measurement error distribution | — | reference |
barndorff2004power |
Bipower variation (jump-robust) | BPV $=\frac{\pi}{2}\sum | r_j | |
barndorff2008designing, barndorff2009realized |
Realized kernels | Noise-robust RV | Needs tick/quote data; with 1-min bars kernels are optional | optional (Tier B sensitivity) |
barndorff2010measuring |
Realized semivariance (RS⁺/RS⁻) | Signed variation | book chapter (OUP) | custom |
hansen2006realized |
RV and microstructure noise; signature plots | Sampling frequency choice | — | proxy sensitivity (1-min vs 5-min) |
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) |
hansen2006consistent |
Consistent ranking requires robust losses | Precursor of Patton (2011) | — | evaluation design |
zhang2005tale, aitsahalia2005how, jacod2009microstructure |
TSRV, optimal sampling, pre-averaging | Noise-robust estimators | Require higher than 1-min frequency to matter | optional sensitivity |
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) |
andersen2005correcting, andersen2011realized |
Forecast evaluation with RV proxies; noise effects | Corrections for proxy error | — | evaluation |
patton2009optimal |
Optimal combinations of RV estimators | — | — | optional |
andersen2010parametric |
Parametric vs nonparametric volatility measurement | Survey | — | reference |
andersen1999forecasting |
Sampling frequency vs forecast horizon | Multi-horizon variance targets | Horizon-matching rationale | design |
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 |
andersen2007roughing |
HAR-CJ (continuous/jump split) | Jumps in HAR | needs BPV | optional |
patton2015good |
HAR with semivariances (HAR-RS) | Signed jumps | — | optional |
bollerslev2016exploiting |
HARQ (measurement-error adjusted) | Time-varying persistence by RQ | needs realized quarticity | optional |
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 |
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) |
engle2006multiple |
MEM (multiplicative error models) | Joint RV/range dynamics | non-GARCH | out of scope |
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 |
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) |
hansen2016exponential |
Realized EGARCH | Log-variance with leverage and multiple RMs | JBES 34(2) 2016 | custom |
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 |
fleming2003economic |
Economic value of volatility timing with RV | Economic loss motivation | — | context (secondary) |
boudt2012highfrequency |
highfrequency R package (CRAN) |
RV, BPV, kernels, HAR, HEAVY | version to be pinned | software |
(c) Multivariate
| bibkey | Model | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
bollerslev1990modelling |
CCC-GARCH | Constant correlation, univariate GARCH margins | PD guaranteed if $R$ PD | rmgarch / custom |
engle1995multivariate |
BEKK | PD by construction; quadratic form | Parameter count $O(N^2)$; scalar/diagonal BEKK for $N>3$ | custom (scalar/diagonal BEKK) |
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) |
tse2002multivariate |
VC-GARCH (Tse–Tsui) | Alternative correlation dynamics | — | out of scope |
cappiello2006asymmetric |
Asymmetric DCC (aDCC) | Correlation asymmetry to joint negative shocks | — | rmgarch (aDCC) |
aielli2013dynamic |
cDCC (corrected DCC) | Consistent DCC estimation | rmgarch implements cDCC; WP46 reports which | rmgarch |
vanderweide2002gogarch |
GO-GARCH | Orthogonal factors with univariate GARCH | Identification via ICA/ML; rmgarch gogarch |
rmgarch |
engle2019large |
DCC-NL (nonlinear shrinkage) | Large-$N$ DCC | For $N\le 10$ baskets not needed | out of scope |
pakel2021fitting |
Composite likelihood for vast DCC | — | — | out of scope |
creal2011dynamic |
Multivariate GAS-t | Score-driven covariance | adjacent | out of scope |
bauwens2006multivariate, silvennoinen2009multivariate |
Surveys | Taxonomy of MGARCH | — | taxonomy |
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) |
patton2009evaluating |
Evaluating volatility and correlation forecasts (handbook chapter) | Multivariate MZ and loss definitions | — | evaluation |
engle2006testing |
Economic value of correlation forecasts (portfolio variance) | Portfolio-based Tier C diagnostic | — | optional |
caporin2014robust |
Robust ranking of MGARCH by dimension | — | — | context |
galanos2013rmgarch |
rmgarch (CRAN) | DCC/aDCC/cDCC/GO-GARCH/copula | pin version | software |
(d) Forecast evaluation and inference
| bibkey | Method | Contribution | Exact-definition caveats | Planned scope |
|---|---|---|---|---|
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 |
hansen2006consistent |
Consistent ranking | Precursor | — | core |
hansen2005forecast |
330 ARCH-type models, DM/$ and IBM, SPA test | Closest predecessor (see §G) | Uses RV proxies, 1-day horizon only | comparator |
hansen2003choosing |
Early MCS application to volatility models | — | — | context |
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 |
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 |
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 |
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)) |
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 |
romano2005stepwise |
StepM multiple testing | FWER control | alternative to SPA | optional |
holm1979simple |
Holm step-down | Simple FWER control for pairwise tables | OpenAlex record (Crossref returns 404 for the JSTOR DOI) | optional |
politis1994stationary, politis2004automatic |
Stationary bootstrap; automatic block length | Bootstrap for SPA/MCS | Patton–Politis–White 2009 correction exists (not cited; see note) | core |
newey1987simple, newey1994automatic |
HAC covariance; automatic lag | DM variance at $h>1$ | — | core |
mincer1969evaluation |
MZ regression $y=a+b\hat h+e$ | Calibration/unbiasedness check | NBER chapter (manual-URL) | secondary |
andersen1998answering, andersen2005correcting |
RV-based $R^2$ and corrections | — | — | secondary |
poon2003forecasting |
Survey of 93 volatility forecasting papers | Historical meta-view | — | related literature |
awartani2005predicting |
S&P 500 GARCH comparison (asymmetries) | Early benchmark | — | comparator |
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 |
bollerslev2018risk |
Risk everywhere (RFS 2018, not JFE) | Cross-asset realized-volatility modelling (50+ futures), HAR-type | — | comparator |
patton2020comparing |
Comparing possibly misspecified forecasts (JBES 2020) | Loss choice matters under misspecification | Reinforces reporting several losses | design |
gneiting2011making, gneiting2007strictly |
Consistent scoring functions; proper scoring rules | Loss/functional consistency | QLIKE is consistent for the conditional variance (Bregman class) | design |
amisano2007comparing, diks2011likelihood |
Weighted likelihood-ratio / tail-weighted density tests | Log-score comparisons when a density is supplied | — | secondary (log score) |
lopez2001evaluating |
Evaluating volatility models (probability-based losses) | — | — | context |
hansen2015equivalence |
OOS comparisons ≡ Wald statistics | Caution on nested OOS tests | — | context |
christoffersen2000how |
Relevance of volatility forecasting for risk management decays with horizon | Horizon 22 relevance | — | context |
kourtis2016international |
Implied vs realized vs GARCH across 13 indices | HAR best at daily horizon | — | comparator |
(e) Tail risk
| bibkey | Method | Contribution | Caveats | Planned scope |
|---|---|---|---|---|
kupiec1995techniques |
Unconditional coverage (POF) test | VaR hit frequency | low power at 1% with short samples | core |
christoffersen1998evaluating |
Conditional coverage / independence (Markov) tests | Clustering of hits | — | core |
christoffersen2004backtesting |
Duration-based backtest | Alternative independence test | author list completed in script | optional |
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 |
berkowitz2011evaluating |
Evaluation of VaR with desk-level data; CAViaR-type tests compared | Power comparison of backtests | — | design |
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) |
patton2019dynamic |
Dynamic semiparametric ES models; FZ0 loss | ES forecast evaluation | — | core (loss definition) |
nolde2017elicitability |
Elicitability and backtesting (comparative vs traditional backtests) | Framework | — | design |
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 |
bayer2022regression, dimitriadis2019joint, bayer2020esback |
Regression-based ES backtests; joint quantile/ES regression; esback |
ESR backtests | JFEC 20(3) 2022 | core (ESR test via R esback) |
taylor2019forecasting |
AL-based joint VaR/ES score | AL log-score as alternative joint loss | JBES 37(1) 2019 | secondary |
ziegel2016coherence |
ES not elicitable alone | Why joint scores are needed | Math. Finance 26(4) 2016 | context |
mcneil2000estimation |
GARCH-EVT | Semi-parametric tails | extension comparator | optional |
kuester2006value |
VaR prediction: comparison of strategies (NASDAQ) | Early tail benchmark; GARCH-EVT/skew-t favoured | JFEC 4(1) 2006 | comparator |
giot2003value |
VaR for long/short positions with skewed-t APARCH | Skewed-t relevance for tails | — | comparator |
(f) Large-scale benchmarks, ML extensions, software
| bibkey | Study | Design | Relation to WP46 |
|---|---|---|---|
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 |
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) |
andersen2006volatility |
Handbook chapter: volatility and correlation forecasting | Survey of methods | related literature |
brownlees2011practical |
Many US assets, GARCH family, QLIKE, multi-step, crisis vs calm | Asymmetric GARCH best overall; calm/storm split | predecessor (regimes) |
ardia2018forecasting |
426 assets, MS-GARCH vs single regime, VaR/ES/density, 2005–2016 | MS helps for tails/density | predecessor (regimes, tails) |
kuester2006value |
VaR strategies on NASDAQ | tails | predecessor (tails) |
liu2015does |
400 RV estimators, 31 assets, QLIKE, MCS | template for proxy choice | predecessor (Tier B proxies) |
laurent2012forecasting |
125 MGARCH, MCS, robust matrix losses | Tier C template | predecessor (Tier C) |
lyocsa2021stock |
HF vs daily information for stock-index volatility | information-set comparison | predecessor (Tier A vs B) |
kourtis2016international |
13 indices, implied/RV/GARCH | HAR dominant daily | predecessor |
christensen2023machine |
ML (trees/NN) vs HAR with many predictors, US equities (JFEC 21(5) 2023) | ML gains with external predictors | ML extension comparator |
bucci2020realized |
Neural networks for RV (JFEC 2020) | — | ML extension |
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 |
rahimikia2024machine, rahimikia2021realised |
ML for RV forecasting (SSRN 2024; arXiv 2021 word-embedding) | working papers (labelled) | ML extension |
branco2024forecasting |
10 indices 2000–2021, linear vs nonlinear ML vs HAR (JEF 2024) | "nothing beats linear models" | 2024 benchmark comparator |
gunnarsson2024prediction |
Review of AI/ML RV and IV prediction (IRFA 2024) | survey of the ML strand | related literature |
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 |
brini2024comparison |
arXiv 2404.04962: crypto vs mature asset classes volatility | crypto context | context |
reisenhofer2022harnet |
HARNet (arXiv 2022) | CNN extension of HAR | ML extension |
kim2018forecasting |
LSTM + GARCH hybrids (ESWA 2018) | hybrid strand | ML extension context |
catania2019forecasting, ardia2019regime, trucios2019forecasting |
Crypto volatility/risk forecasting (GARCH/MS-GARCH, robust) | crypto block references | design (crypto instruments) |
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) |
galanos2011rugarch, galanos2013rmgarch |
rugarch / rmgarch CRAN records (DOIs registered by CRAN; issued = first release) |
R reference libraries (1.5-6) | software |
ardia2019markov, ardia2016msgarch |
MSGARCH JSS + CRAN | — | software |
ardia2019generalized |
GAS package JSS | — | software (optional) |
boudt2012highfrequency |
highfrequency CRAN | — | software |
catania2014mcs |
MCS R package (CRAN) | MCS implementation cross-check | software (optional; WP46 implements MCS in Python and cross-checks) |
bayer2020esback |
esback CRAN | ES backtests | software |
Definition caveats that WP46 must not blur (C1)
- 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.archhas no Zakoïan TGARCH (itsGARCH(p,o,q)is GJR; itsAPARCHwith $\delta=1$ reproduces Zakoïan). WP46 names:gjrandtgarch_zakoian. - EGARCH parameterisations differ across Nelson (1991),
archand 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. - NGARCH vs NAGARCH. Higgins–Bera (1992) is a power/Box–Cox nonlinearity; Engle–Ng (1993) NAGARCH shifts the news-impact curve. rugarch
fGARCHhas both as distinct submodels. - 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 vianelson1992inequality/conrad2006inequality. - Component GARCH has two common parameterisations (Engle–Lee permanent/transitory vs the equivalent rugarch
csGARCH); forecasts coincide but constraints are written differently. - 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 ofbauwens2010theory. - 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. - DCC vs cDCC (
aielli2013dynamic): rmgarch estimates cDCC by default; report which. - Skewed Student-t means Hansen (1994) in
archand Fernández–Steel (1998) in rugarch; densities and skewness parameters are not interchangeable (brief: "reconcile probability density conventions"). - 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).
- 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. - RiskMetrics $\lambda=0.94$ (1996) vs RM2006 multi-scale kernel (
zumbach2009riskmetrics) are different baselines. - 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).
- 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.
G. Closest large-scale benchmarks and incremental contribution
| Study | Assets / period | Models | Horizons | Losses / inference | Tiers | Failure & compute accounting | Pre-registration |
|---|---|---|---|---|---|---|---|
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 |
marcucci2005forecasting |
S&P 100 (1 series) | MS-GARCH vs GARCH/EGARCH/GJR | 1, 5, 10, 22 | several losses, SPA | daily | none | none |
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 |
ardia2018forecasting |
426 stocks/indices/FX, 2005–2016 | MS-GARCH vs single-regime | 1 | VaR/ES/density scores, MCS | daily | none | none |
kuester2006value |
NASDAQ (1 series) | GARCH-type, EVT, CAViaR, skew-t | 1 | VaR backtests | daily | none | none |
liu2015does |
31 assets (ETFs, stocks, FX, futures) | 400 RV estimators | — | QLIKE, MCS | realized | none | none |
laurent2012forecasting |
10 US stocks | 125 MGARCH | 1 | consistent matrix losses, MCS | multivariate | none | none |
lyocsa2021stock |
stock indices | HAR vs GARCH-type | 1–22 | QLIKE/MSE, MCS | daily vs HF | none | none |
christensen2023machine |
US stocks (RV) + predictors | ML vs HAR | 1, 5, 22 | MSE/QLIKE, DM/MCS | realized | none | none |
zhang2024volatility |
US stocks (RV, intraday commonality) | ML vs HAR/OLS | 1 (+) | MSE/QLIKE, MCS | realized | none | none |
branco2024forecasting |
10 indices, 2000–2021 | linear vs ML vs HAR | 1, 5, 22 | losses, MCS, econ. value | realized | none | none |
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 |
| 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) |
What is new (relative to the table).
- 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. - 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.
- 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.
- Definition-faithful taxonomy (C1) with per-architecture model cards and cross-package likelihood checks; the comparators rely on one package's naming.
- 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.
What is not new (and must be said so in the paper).
- 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).
- 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.
- Regime-dependence of model rankings is documented by Marcucci (2005), Brownlees–Engle–Kelly (2011) and Ardia et al. (2018).
- Horizons 1/5/22 and QLIKE-with-MCS are the standard design of the 2023–2026 realized-volatility/ML benchmarks.
- Multivariate loss consistency and MCS for MGARCH are Laurent–Rombouts–Violante (2012, 2013).
- 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.
- 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.
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.
Search log (all on 2026-11-09)
| Tool | Query / request | Outcome |
|---|---|---|
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) |
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 |
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) |
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 |
| Zenodo API | records/17404619 | arch v8.0.0, 2025-10-21, DOI 10.5281/zenodo.17404619, concept 10.5281/zenodo.593254 |
| 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 |
| curl | MSCI PDF of the RiskMetrics Technical Document (HTTP 200, application/pdf; cover page read with pdftotext) | confirmed |
| WebSearch | "volatility forecasting benchmark GARCH 2024 'does anything beat' large-scale comparison" | only Hansen–Lunde 2005 + a 2024 HEC Montréal master's thesis |
| WebSearch | "'Forecasting realized volatility: Does anything beat linear models?' Branco Rubesam Zevallos" | JEF 78 (2024), DOI 10.1016/j.jempfin.2024.101524 |
| WebSearch | "model confidence set volatility models 2023 cross-asset GARCH realized GARCH HAR forecast comparison 2025" | Kourtis–Markellos–Symeonidis 2016 (JFM); theses |
| 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 |
| WebSearch | "GARCH(1,1) versus machine learning volatility forecasting large cross-section 2025 …" | working papers/theses only; no journal benchmark |
| WebSearch | "'does anything beat a GARCH' 2023 OR 2024 OR 2025 revisited twenty years later volatility forecast" | nothing after 2005 |
| WebSearch | "Sheppard arch Python package Zenodo DOI bashtage/arch latest release 2025" | Zenodo 17404619 (v8.0.0) |
| 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) |
| WebSearch | Engle & Lee 1999 Festschrift chapter | OUP chapter 20, pp. 475–497, title "A Long-Run and Short-Run Component Model…" |
| WebSearch | Acerbi–Székely 2014 Risk magazine | Risk.net technical paper 2381658 (abstract only) |
| 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 |
MCP note: the openalex and anthropic MCP servers failed to connect in this session; OpenAlex was queried through its public REST API with curl instead.
Unverified / not found / caveats on verified items
| Item | Status | Detail |
|---|---|---|
| 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. |
| 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)". |
| 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. |
| Harvey & Chakravarty (2008) Beta-t-(E)GARCH | manual-URL (EconPapers) | Cambridge WP 0840; the published successor used is harvey2014egarch (CSDA) and the book harvey2013dynamic. |
| Mincer & Zarnowitz (1969) | manual-URL (NBER) | Page range not shown on the NBER chapter page → omitted. |
| J.P. Morgan/Reuters (1996) RiskMetrics Technical Document | manual-URL (MSCI PDF) | Cover page read; cited as @techreport. |
Sheppard arch |
manual (Zenodo API) | DataCite DOI, not Crossref. |
| 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. |
| 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. |
| Fissler, Ziegel & Gneiting | verified via arXiv (2015) | bibkey fissler2015expected (arXiv v1, 2015-07-01); the Risk magazine 2016 version has no registry record. |
| 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. |
| Bollerslev, Hood, Huss & Pedersen (2018) | verified | Published in RFS 31(7), not JFE as stated in the task list. |
| Brownlees, Engle & Kelly (2011) | verified | Journal of Risk 14(2), 2011/12 (not JFEC). |
| Patton (2020) | verified | JBES 38(4), 2020 (Crossref issued 2019 = online). |
| Engle & Sokalska | verified | JFEC 9(1), 2011 (not 2012). |
| "Zhang, Zohren et al. 2024" (task list) | corrected | The JFEC 2024 intraday-commonality paper is Zhang, Zhang, Cucuringu & Qian; Zohren co-authors rahimikia2021realised (arXiv). |
| "Lunde & Hansen comparisons" (task list) | interpreted | Covered by hansen2005forecast, hansen2006consistent, hansen2005realized, hansen2003choosing. |
| Zumbach RM2006 | verified as SSRN posting (2009) | bibkey year follows the registry record; original RiskMetrics Group document is 2007. |
| Patton, Politis & White (2009) correction to Politis–White | not added | not required for the design; add if the automatic block length is used verbatim. |
| 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. |
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). |
| JSS/SNDE articles without page numbers | verified | ardia2019markov, ardia2019generalized, gonzalezrivera1998smooth, marcucci2005forecasting use article numbers (Crossref has no page). |