\begin{table}[htbp]\centering\scriptsize
\caption{Baseline specifications (information set = completed bars at the origin; tuned on training/validation periods only)}
\label{tab:baselines}
\begin{tabular}{p{2.6cm}p{12.5cm}}
\toprule
Model & Specification \\
\midrule
Random walk & window: 390 one-minute bars; distribution: Gaussian, zero mean, scale = trailing RMS one-minute return x sqrt(H) \\
Seasonal volatility & profile: past-20-session mean squared return per slot (past only); level\_adjustment: trailing 30-minute RV over the seasonal counterpart, clipped to [0.25, 4] \\
EWMA-$t$ & lambda: 0.97 per minute; nu: 5; history: last 3 sessions of one-minute returns \\
HAR-RV & regressors: log RV 30 min, log RV 390 min, log RV 5 days, time of day, time of day squared, log H; fit: OLS on training origins, one regression per horizon; nu: method of moments on standardised training residuals, clipped to [2.5, 50] \\
GARCH(1,1)-$t$ & model: GARCH(1,1) with Student-t innovations on 5-minute training returns, one fit per instrument (arch 8); forecast: analytic variance term structure over ceil(H/5) steps; own filter over the last 400 five-minute returns \\
Ridge & alpha: 1.0; features: 19 origin features (src/chronos\_x/baselines/features.py); targets: scaled cumulative return (location) and log scaled realised variance (scale); nu from residual kurtosis \\
Elastic net & alpha: 0.001; l1\_ratio: 0.5 \\
LightGBM & n\_estimators: 400; learning\_rate: 0.03; num\_leaves: 31; subsample: 0.8; colsample\_bytree: 0.8 \\
MLP & inputs: last 60 one-minute bars (15 features each) + 9 global features + future calendar; hidden: 256 x 2 (GELU, dropout 0.1); head: Student-t per future minute, masked NLL \\
TCN & channels: 96; blocks: 6 dilated causal convolutions (kernel 3, dilation 1..32) over 390 one-minute bars; head: Student-t per future minute, masked NLL \\
\midrule
Not run & \emph{chronos\_timesfm}: pretrained foundation models not evaluated: weights not available offline on the compute node; tokenisers assume a single real-valued series without missingness masks; licenses/terms not reviewed within this project; \emph{egarch}: multi-step forecasts require simulation; too slow for the number of evaluation origins; GARCH(1,1)-t reported; \emph{patchtst\_itransformer}: the one-minute-only MRPT variant is the equal-parameter patch-transformer control; iTransformer not implemented \\
\bottomrule
\end{tabular}
\end{table}