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Jonathan Berrisch
2025-06-14 15:24:22 +02:00
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@@ -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
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@@ -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**).
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@@ -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
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</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.
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