1\begin{tabular}{llllll}2\toprule3Architecture & Family & Seminal reference & Innovations & Implementation & Multi-step \\4\midrule5Constant, hist.\ 22/66/252, EWMA, RM2006 & baseline & \citet{jpmorgan1996riskmetrics,zumbach2009riskmetrics} & N / empirical & arch / ols & flat / analytic \\6ARCH(5) & classical & \citet{engle1982autoregressive} & N, $t$, GED, skt & arch & analytic \\7GARCH(1,1), (2,1), (1,2) & classical & \citet{bollerslev1986generalized} & N, $t$, GED, skt & arch & analytic \\8IGARCH(1,1) & classical & \citet{engle1986modelling} & N, $t$, GED, skt & custom & analytic \\9GARCH-M(1,1) & classical & \citet{engle1987estimating} & N, $t$, GED, skt & custom & analytic \\10GJR(1,1) & asymmetric & \citet{glosten1993relation} & N, $t$, GED, skt & arch & analytic ($\kappa$) \\11TGARCH(1,1) (Zakoïan) & asymmetric & \citet{zakoian1994threshold} & N, $t$, GED, skt & arch & simulation \\12EGARCH(1,1) & asymmetric & \citet{nelson1991conditional} & N, $t$, GED, skt & arch & simulation \\13NAGARCH(1,1) & asymmetric & \citet{engle1993measuring} & N, $t$, GED, skt & custom & analytic \\14QGARCH(1,1) & asymmetric & \citet{sentana1995quadratic} & N, $t$, GED, skt & custom & analytic \\15AVGARCH(1,1) & power & \citet{taylor2008modelling,schwert1989why} & N, $t$, GED, skt & arch & simulation \\16APARCH(1,1) & power & \citet{ding1993long} & N, $t$, GED, skt & arch & simulation \\17FIGARCH(1,$d$,1) & fractional & \citet{baillie1996fractionally} & N, $t$, GED, skt & arch & analytic \\18FIEGARCH, FIAPARCH, HYGARCH & fractional & \citet{bollerslev1996modeling,tse1998conditional,davidson2004moment} & --- & unsupported & --- \\19Component GARCH & component & \citet{engle1999long} & N, $t$, GED, skt & custom & analytic \\20MS-GARCH(2) & regime switching & \citet{haas2004new} & N, $t$ & custom & analytic (HMP) \\21ST-GARCH, GARCH-MIDAS & regime / component & \citet{gonzalezrivera1998smooth,engle2013stock} & --- & unsupported & --- \\22GAS-$t$(1,1) & score-driven & \citet{creal2013generalized} & $t$ & custom & analytic \\23Stochastic volatility & parameter-driven & \citet{kim1998stochastic} & --- & unsupported & --- \\24\midrule25RV random walk, HAR, log-HAR & realized & \citet{corsi2009simple} & empirical & ols & direct \\26GARCH-X(1,1) & realized & \citet{engle2002new} & N, $t$ & custom & analytic \\27HEAVY(1,1) & realized & \citet{shephard2010realising} & N, $t$ & custom & analytic \\28Realized GARCH(1,1) & realized & \citet{hansen2012realized} & N, $t$ & custom & simulation \\29Realized EGARCH & realized & \citet{hansen2016exponential} & --- & unsupported & --- \\30\midrule31Rolling cov., EWMA cov., CCC, DCC, aDCC, scalar BEKK & multivariate & \citet{bollerslev1990modelling,engle2002dynamic,cappiello2006asymmetric,engle1995multivariate} & N (QML) & custom & $h=1$ \\32\bottomrule33\end{tabular}34