diff --git a/assets/voldep/frame.svg b/assets/voldep/frame.svg new file mode 100644 index 0000000..3deb84d --- /dev/null +++ b/assets/voldep/frame.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/index.html b/index.html index 00e63c9..7321ad6 100644 --- a/index.html +++ b/index.html @@ -25896,7 +25896,7 @@ Berrisch, J. (Introduction
-

The Idea:

+

The Idea:
@@ -26039,12 +26039,12 @@ w_{t,k}^{\text{Naive}} = \frac{1}{K}\label{eq:naive_combination}

\[\begin{equation} \frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\min} \right) \stackrel{t\to \infty}{\rightarrow} a \quad \text{with} \quad a \leq 0. \label{eq_opt_select} -\end{equation}\] The forecaster is asymptotically not worse than the best expert \(\widehat{\mathcal{R}}_{t,\min}\).

+\end{equation}\] The forecaster is asymptotically not worse than the best expert.

The convex aggregation problem

\[\begin{equation} \frac{1}{t}\left(\widetilde{\mathcal{R}}_t - \widehat{\mathcal{R}}_{t,\pi} \right) \stackrel{t\to \infty}{\rightarrow} b \quad \text{with} \quad b \leq 0 . \label{eq_opt_conv} -\end{equation}\] The forecaster is asymptotically not worse than the best convex combination \(\widehat{X}_{t,\pi}\) in hindsight (oracle).

+\end{equation}\] The forecaster is asymptotically not worse than the best convex combination in hindsight (oracle).

@@ -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}\]

-

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.

Almost optimal w.r.t. selection \(\eqref{eq_optp_select}\) Gaillard & Wintenberger (2018).

We show that this holds for QL under feasible conditions.

@@ -28148,11 +28148,10 @@ Coal
-


- +
-

Berrisch, Pappert, et al. (2023)

+

Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. (2023). Modeling volatility and dependence of European carbon and energy prices. Finance Research Letters, 52, 103503.

diff --git a/index.qmd b/index.qmd index f02040a..583fc03 100644 --- a/index.qmd +++ b/index.qmd @@ -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. 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%"} -
-
- +
- @berrisch2023modeling + Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. [-@berrisch2023modeling]. Modeling volatility and dependence of European carbon and energy prices. Finance Research Letters, 52, 103503. :::