spb/wp7_uqo

1\begin{table}[H]2\centering3\caption{Out-of-sample realized-variance forecasting: HAR-RV against IV-surface models.}4\label{tab:rq2_oos}5\begin{threeparttable}6\footnotesize7\begin{tabular}{@{}lrrrrr@{}}8\toprule9& \multicolumn{2}{c}{$R^2_{OOS}$} & \multicolumn{2}{c}{QLIKE} & \\10\cmidrule(lr){2-3}\cmidrule(lr){4-5}11Model & Median & Mean & Median & Mean & $R^2_{OOS}>0$ \\12\midrule13\multicolumn{6}{@{}l}{\textit{Panel A: target $RV_{t+1}$}} \\14$RV_t + r_t^2$ (ARCH-type) & 0.212 & 0.194 & 0.308 & 0.297 & 28/30 \\15HAR-RV & 0.241 & 0.248 & 0.296 & 0.285 & 28/30 \\16IV only (30d, 90d) & 0.227 & 0.227 & 0.354 & 0.355 & 30/30 \\17IV surface & 0.204 & 0.202 & 0.408 & 0.453 & 28/30 \\18HAR-RV $+$ IV surface & 0.309 & 0.296 & 0.341 & 0.350 & 29/30 \\19\multicolumn{6}{@{}l}{\quad HAR-RV $+$ IV surface vs.\ HAR-RV: median MSE ratio 0.967, DM$_{MSE}>1.96$ for 14/30 tickers, $<-1.96$ for 0; } \\20\multicolumn{6}{@{}l}{\quad median QLIKE ratio 1.171, DM$_{QLIKE}>1.96$ for 0/30, $<-1.96$ for 15.} \\21\addlinespace22\multicolumn{6}{@{}l}{\textit{Panel B: target $\sum_{j=1}^{5} RV_{t+j}$}} \\23$RV_t + r_t^2$ (ARCH-type) & 0.128 & 0.112 & 0.262 & 0.254 & 26/30 \\24HAR-RV & 0.204 & 0.184 & 0.247 & 0.240 & 26/30 \\25IV only (30d, 90d) & 0.276 & 0.260 & 0.220 & 0.235 & 30/30 \\26IV surface & 0.235 & 0.209 & 0.248 & 0.302 & 28/30 \\27HAR-RV $+$ IV surface & 0.264 & 0.241 & 0.246 & 0.264 & 29/30 \\28\multicolumn{6}{@{}l}{\quad HAR-RV $+$ IV surface vs.\ HAR-RV: median MSE ratio 0.941, DM$_{MSE}>1.96$ for 8/30 tickers, $<-1.96$ for 1; } \\29\multicolumn{6}{@{}l}{\quad median QLIKE ratio 1.001, DM$_{QLIKE}>1.96$ for 6/30, $<-1.96$ for 5.} \\30\bottomrule31\end{tabular}32\begin{tablenotes}[flushleft]\footnotesize33\item \textit{Notes.} Rolling-window forecasts for the 30 tickers with the longest histories: each model is re-estimated by OLS on 500 trading days and used for the next 250 days, the window then advancing by 250 days; the stacked forecasts yield per-ticker $R^2_{OOS}=1-\sum(RV-\widehat{RV})^2/\sum(RV-\overline{RV})^2$ and QLIKE $=\frac{1}{T}\sum[RV/\widehat{RV}-\ln(RV/\widehat{RV})-1]$ \citep{patton2011volatility}. Columns report the median and mean across tickers and the number of tickers with positive $R^2_{OOS}$. Diebold--Mariano statistics \citep{diebold1995comparing} are computed per ticker on the loss differential with Newey--West variance ($h$ lags); positive values favour the IV-augmented model. Per-ticker statistics are in Table~\ref{tab:app_dm}.34\end{tablenotes}35\end{threeparttable}36\end{table}37