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PhD thesis — Three essays on high-frequency return and volatility dynamics in commodities and financial futures markets (Université Laval).

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1\section{Additional Tables and Figures}2\label{sec:app_additional}34This appendix collects supplementary tables and figures that support the main results but are not essential for following the core argument.56\subsection{Descriptive Figures}78\begin{figure}[H]9\centering10\includegraphics[width=0.85\textwidth]{figures/figD1_return_density.pdf}11\caption{Distribution of 1-minute log returns on FOMC days. Winsorized at 0.5\% tails for display. The heavy tails and leptokurtic shape are consistent with the Jarque--Bera test rejections reported in Table~\ref{tab:desc_1min_ret}.}12\label{fig:D1}13\end{figure}1415\begin{figure}[H]16\centering17\includegraphics[width=0.85\textwidth]{figures/figD5_acf_returns.pdf}18\caption{Autocorrelation of 1-minute returns. Grey band shows 95\% confidence interval. Negative first-order autocorrelation reflects bid--ask bounce effects typical of high-frequency data.}19\label{fig:D5}20\end{figure}2122\begin{figure}[H]23\centering24\includegraphics[width=0.85\textwidth]{figures/figD8b_log_rv_distribution.pdf}25\caption{Distribution of $\log(\mathrm{RV})$. Near-Gaussian shape validates the use of $\log(\mathrm{RV})$ as the dependent variable in the panel regressions.}26\label{fig:D8b}27\end{figure}2829\subsection{Ensemble Model Diagnostics}3031\begin{figure}[H]32\centering33\includegraphics[width=0.6\textwidth]{figures/pca_axis_quality.png}34\caption{PCA axis assignment quality. Bar height shows $|\text{Corr}|$ between PC projection and keyword differential. All axes exceed the 0.04 minimum separation threshold.}35\label{fig:pca_quality}36\end{figure}3738\begin{figure}[H]39\centering40\begin{subfigure}[b]{0.48\textwidth}41\includegraphics[width=\textwidth]{figures/novelty_comparison.png}42\caption{Novelty: MiniLM vs BERT}43\end{subfigure}44\hfill45\begin{subfigure}[b]{0.48\textwidth}46\includegraphics[width=\textwidth]{figures/scatter_comparison.png}47\caption{Score scatter plots}48\end{subfigure}49\caption{Model comparison: MiniLM (384d) vs.\ BERT (768d). Novelty correlation $r = 0.72$; policy stance tone $r = 0.56$. The moderate inter-model correlation supports the use of an ensemble approach.}50\label{fig:model_comparison}51\end{figure}5253\begin{figure}[H]54\centering55\begin{subfigure}[b]{0.48\textwidth}56\includegraphics[width=\textwidth]{figures/tone_comparison.png}57\caption{Tone comparison across models}58\end{subfigure}59\hfill60\begin{subfigure}[b]{0.48\textwidth}61\includegraphics[width=\textwidth]{figures/confidence_distribution.png}62\caption{Ensemble confidence distribution}63\end{subfigure}64\caption{Tone model comparison and confidence diagnostics. The right panel shows that ensemble confidence is concentrated above 0.7, indicating strong inter-model agreement for most statements.}65\label{fig:tone_conf}66\end{figure}6768\subsection{Additional Panel Regression Tables}6970Tables~\ref{tab:panel_rv_stance}--\ref{tab:panel_return_novelty} report panel minute-level regressions for the remaining dependent variables (realized volatility in levels, realized beta, and returns), separately for stance and novelty.7172\input{tables/tableP_panel_rv_stance.tex}73\input{tables/tableP_panel_rv_novelty.tex}74\input{tables/tableP_panel_beta_stance.tex}75\input{tables/tableP_panel_beta_novelty.tex}76\input{tables/tableP_panel_return_stance.tex}77\input{tables/tableP_panel_return_novelty.tex}7879\subsection{Additional Event-Level Regression Tables}8081Tables~\ref{tab:rolling_rv_ratio_30min} and~\ref{tab:rolling_log_rv_ratio_30min} report the event-level RV-ratio specifications, which corroborate the pre/post difference results in the main text.8283\input{tables/tableR_rv_ratio_30min.tex}84\input{tables/tableR_log_rv_ratio_30min.tex}8586\subsection{Additional IRF and Drift Figures}8788\begin{figure}[H]89\centering90\includegraphics[width=0.85\textwidth]{figures/figR9_drift_by_novelty.pdf}91\caption{Cumulative return drift by novelty tercile. Unlike stance-based drift (Figure~\ref{fig:R8}), novelty terciles show less directional separation, consistent with novelty affecting volatility rather than returns.}92\label{fig:R9}93\end{figure}9495\begin{figure}[H]96\centering97\includegraphics[width=0.85\textwidth]{figures/figR10_irf_ret_h_novelty.pdf}98\caption{Impulse response: cumulative return to novelty. Effects are generally smaller and less significant than stance effects (Figure~\ref{fig:R10_stance}), supporting the hypothesis that novelty operates through volatility rather than returns.}99\label{fig:R10_novelty}100\end{figure}101102\begin{figure}[H]103\centering104\includegraphics[width=0.85\textwidth]{figures/figR10b_irf_placebo_novelty.pdf}105\caption{Pre-announcement placebo: IRF for novelty. All coefficients are near zero, corroborating the placebo results for stance (Figure~\ref{fig:placebo_stance}).}106\label{fig:placebo_novelty}107\end{figure}108109\subsection{Sub-Period Stability}110111\begin{figure}[H]112\centering113\includegraphics[width=0.85\textwidth]{figures/figRob_subperiod_heatmap.pdf}114\caption{Sub-period stability: regression coefficients across six Fed policy regimes. Coefficient signs are generally consistent across sub-periods, though magnitudes vary with the degree of policy uncertainty in each regime.}115\label{fig:rob_subperiod}116\end{figure}117