\section{Additional tables}\label{app:extra}

\subsection{All innovation laws, trimmed and median ratios}
Table~\ref{tab:pooledAfull} reports the pooled ratios of every Tier~A specification (all innovation laws), and
Table~\ref{tab:pooledAfullrobust} the 1\%-trimmed and median ratios together with the share of explosive forecasts
(cumulative forecast above one hundred times the trailing 22-day mean of the proxy at the origin).

\begin{table}[htp]\centering\tiny
\caption{Tier A, all specifications: pooled QLIKE ratios to GARCH(1,1)-normal (test period). Columns as in Table~\ref{tab:pooledA}.}\label{tab:pooledAfull}
\adjustbox{max width=\textwidth}{\input{tables/tab_pooled_tierA}}
\end{table}

\begin{table}[htp]\centering\tiny
\caption{Robust summaries, $h=1$ and $h=22$: 1\%-trimmed and median pooled ratios and explosive-forecast shares.}\label{tab:pooledAfullrobust}
\adjustbox{max width=\textwidth}{\input{tables/tab_pooled_robust}}
\end{table}

\subsection{Model confidence sets over all specifications}
\begin{figure}[htp]\centering
\includegraphics[width=\textwidth]{figures/fig_mcs_h1_tierA.pdf}
\caption{90\% MCS per instrument over all Tier A specifications (pre-registered set), $h=1$.}\label{fig:mcsA}
\end{figure}
\begin{figure}[htp]\centering
\includegraphics[width=\textwidth]{figures/fig_mcs_h22_tierA.pdf}
\caption{90\% MCS per instrument over all Tier A specifications (pre-registered set), $h=22$.}\label{fig:mcsA22}
\end{figure}

\subsection{Regimes at the monthly horizon}
\begin{table}[htp]\centering\scriptsize
\caption{Pooled QLIKE ratios by regime, $h=22$ (conventions as in Table~\ref{tab:regimes}).}\label{tab:regimes22}
\adjustbox{max width=\textwidth}{\input{tables/tab_regimes_h22}}
\end{table}

\subsection{Secondary proxies and losses}
\begin{table}[htp]\centering\tiny
\caption{Pooled ratios to GARCH(1,1)-normal under the secondary proxies (QLIKE) and the secondary losses (primary proxy), $h=1$,
representative specifications.}\label{tab:secondary}
\adjustbox{max width=\textwidth}{\input{tables/tab_secondary}}
\end{table}

\subsection{Cross-package verification}
See Table~\ref{tab:crosscheck} in Appendix~\ref{app:verification}.

\subsection{Tier C diagnostics}
Minimum eigenvalue of the one-step covariance forecasts over all origins: equity basket 0.0032 (EWMA) to 0.0069 (rolling);
cross-asset basket 0.033 (EWMA) to 0.088 (BEKK). All positive: every forecast is positive definite.