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BerriJ committed 2025-06-14 15:24:22 +02:00
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index.html
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@@ -25896,7 +25896,7 @@ Berrisch, J. <span class="citation" data-cites="berrisch2025rcpptimer">(<a href=
<h2>Introduction</h2>
<div class="columns">
<div class="column" style="width:48%;">
<p>The Idea:</p>
<h3 id="the-idea">The Idea:</h3>
<ul>
<li><p>Combine multiple forecasts instead of choosing one</p></li>
<li><p>Combination weights may vary over <strong>time</strong>, over the <strong>distribution</strong> or <strong>both</strong></p></li>
@@ -25965,7 +25965,7 @@ Berrisch, J. <span class="citation" data-cites="berrisch2025rcpptimer">(<a href=
<ul>
<li>The experts can be institutions, persons, or models</li>
<li>The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions</li>
<li>We do not need any assumptions concerning the underlying data</li>
<li>We do not need a distributional assumption concerning the underlying data</li>
<li><span class="citation" data-cites="cesa2006prediction">Cesa-Bianchi &amp; Lugosi (<a href="#/references" role="doc-biblioref" onclick>2006</a>)</span></li>
</ul>
</div></div>
@@ -26039,12 +26039,12 @@ w_{t,k}^{\text{Naive}} = \frac{1}{K}\label{eq:naive_combination}
<p><span class="math display">\[\begin{equation}
\frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\min} \right) \stackrel{t\to \infty}{\rightarrow} a \quad \text{with} \quad a \leq 0.
\label{eq_opt_select}
\end{equation}\]</span> The forecaster is asymptotically not worse than the best expert <span class="math inline">\(\widehat{\mathcal{R}}_{t,\min}\)</span>.</p>
\end{equation}\]</span> The forecaster is asymptotically not worse than the best expert.</p>
<h3 id="the-convex-aggregation-problem">The convex aggregation problem</h3>
<p><span class="math display">\[\begin{equation}
\frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\pi} \right) \stackrel{t\to \infty}{\rightarrow} b \quad \text{with} \quad b \leq 0 .
\label{eq_opt_conv}
\end{equation}\]</span> The forecaster is asymptotically not worse than the best convex combination <span class="math inline">\(\widehat{X}_{t,\pi}\)</span> in hindsight (<strong>oracle</strong>).</p>
\end{equation}\]</span> The forecaster is asymptotically not worse than the best convex combination in hindsight (<strong>oracle</strong>).</p>
</div><div class="column" style="width:4%;">
</div><div class="column" style="width:48%;">
@@ -26122,7 +26122,7 @@ w_{t,k}^{\text{Naive}} = \frac{1}{K}\label{eq:naive_combination}
1-2e^{-x}
\label{eq_boa_opt_select}
\end{equation}\]</span></p>
<p>if <span class="math inline">\(Y_t\)</span> is bounded, the considered loss <span class="math inline">\(\ell\)</span> is convex <span class="math inline">\(G\)</span>-Lipschitz and weak exp-concave in its first coordinate.</p>
<p>if <span class="math inline">\(Y_t\)</span> is bounded, the considered loss <span class="math inline">\(\ell\)</span> is convex, <span class="math inline">\(G\)</span>-Lipschitz, and weak exp-concave in its first coordinate.</p>
<p><i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_10);"></i> Almost optimal w.r.t. <em>selection</em> <span class="math inline">\(\eqref{eq_optp_select}\)</span> <span class="citation" data-cites="gaillard2018efficient">Gaillard &amp; Wintenberger (<a href="#/references" role="doc-biblioref" onclick>2018</a>)</span>.</p>
<p><i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_10);"></i> We show that this holds for QL under feasible conditions.</p>
</div>
@@ -28148,11 +28148,10 @@ Coal
</div><div class="column" style="width:4%;">
</div><div class="column" style="width:48%;">
<p><br></p>
<center>
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src="data:image/svg+xml;base64,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 truncated
</center>
<p><i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_10);"></i> <span class="citation" data-cites="berrisch2023modeling">Berrisch, Pappert, et al. (<a href="#/references" role="doc-biblioref" onclick>2023</a>)</span></p>
<p><i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> Berrisch, J., Pappert, S., Ziel, F., &amp; Arsova, A. <span class="citation" data-cites="berrisch2023modeling">(<a href="#/references" role="doc-biblioref" onclick>2023</a>)</span>. Modeling volatility and dependence of European carbon and energy prices. <em>Finance Research Letters</em>, 52, 103503.</p>
</div></div>
</section>
<section id="sec-contributions" class="slide level2">
index.qmd
+7 -9
View File
@@ -765,7 +765,7 @@ Berrisch, J., & Ziel, F. [-@BERRISCH2023105221]. *Journal of Econometrics*, 237(
::: {.column width="48%"}
The Idea:
### The Idea:
- Combine multiple forecasts instead of choosing one
@@ -958,7 +958,7 @@ Each day, $t = 1, 2, ... T$
- The experts can be institutions, persons, or models
- The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions
- We do not need any assumptions concerning the underlying data
- We do not need a distributional assumption concerning the underlying data
- @cesa2006prediction
:::
@@ -1080,7 +1080,7 @@ In stochastic settings, the cumulative Risk should be analyzed @wintenberger2017
\frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\min} \right) \stackrel{t\to \infty}{\rightarrow} a \quad \text{with} \quad a \leq 0.
\label{eq_opt_select}
\end{equation}
The forecaster is asymptotically not worse than the best expert $\widehat{\mathcal{R}}_{t,\min}$.
The forecaster is asymptotically not worse than the best expert.
### The convex aggregation problem
@@ -1088,7 +1088,7 @@ The forecaster is asymptotically not worse than the best expert $\widehat{\mathc
\frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\pi} \right) \stackrel{t\to \infty}{\rightarrow} b \quad \text{with} \quad b \leq 0 .
\label{eq_opt_conv}
\end{equation}
The forecaster is asymptotically not worse than the best convex combination $\widehat{X}_{t,\pi}$ in hindsight (**oracle**).
The forecaster is asymptotically not worse than the best convex combination in hindsight (**oracle**).
:::
@@ -1209,7 +1209,7 @@ The same algorithm satisfies that there exist a $C>0$ such that for $x>0$ it hol
\label{eq_boa_opt_select}
\end{equation}
if $Y_t$ is bounded, the considered loss $\ell$ is convex $G$-Lipschitz and weak exp-concave in its first coordinate.
if $Y_t$ is bounded, the considered loss $\ell$ is convex, $G$-Lipschitz, and weak exp-concave in its first coordinate.
<i class="fa fa-fw fa-arrow-right" style="color:var(--col_grey_10);"></i> Almost optimal w.r.t. *selection* \eqref{eq_optp_select} @gaillard2018efficient.
@@ -3649,13 +3649,11 @@ Accounting for heteroscedasticity or stabilizing the variance via log transforma
::: {.column width="48%"}
</br>
<center>
<img src="assets/voldep/frame.png">
<img src="assets/voldep/frame.svg" width="250">
</center>
<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_10);"></i> @berrisch2023modeling
<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. [-@berrisch2023modeling]. Modeling volatility and dependence of European carbon and energy prices. <em>Finance Research Letters</em>, 52, 103503.
:::