From 6b1b6aea206016b1667cfbb7d5421bd4c2fe60be Mon Sep 17 00:00:00 2001 From: Jonathan Berrisch Date: Sun, 22 Jun 2025 16:45:20 +0200 Subject: [PATCH] Update slides --- index.html | 403 ++++++++++++++++++++++++++--------------------------- index.qmd | 33 ++--- 2 files changed, 208 insertions(+), 228 deletions(-) diff --git a/index.html b/index.html index 94e5392..4d7cfea 100644 --- a/index.html +++ b/index.html @@ -26162,28 +26162,22 @@ Berrisch, J. (

The Framework of Prediction under Expert Advice

 

-
-

Each day, \(t = 1, 2, ... T\)

  • The forecaster receives predictions \(\widehat{X}_{t,k}\) from \(K\) experts
  • The forecaster assigns weights \(w_{t,k}\) to each expert
    • -
  • The forecaster calculates her prediction: \[\begin{equation} - \widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}. - \label{eq_forecast_def} -\end{equation}\]
    • +
  • The forecaster calculates the prediction:
    • +
+

\[\begin{equation} + \widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}. + \label{eq_forecast_def} +\end{equation}\]

+
  • The realization for \(t\) is observed
-
- -
- -
+

The experts can be institutions, persons, or models

+

The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions

+

Cesa-Bianchi & Lugosi (2006)

The Regret

@@ -27226,7 +27220,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
- +
@@ -27234,194 +27228,194 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
-
@@ -27529,7 +27523,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

Motivation

-

Understanding European Allowances (EUA) dynamics is important for several fields:

+

Understanding European Emission Allowances (EUA)

Portfolio & Risk Management,

Sustainability Planing

Political decisions

@@ -27607,8 +27601,9 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

\[\mathbf{F} = (F_1, \ldots, F_K)^{\intercal}\]

Generalized non-central t-distributions

    -
  • Time varying: expectation \(\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}\) +
  • Time varying:
      +
    • expectation \(\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}\)
    • variance: \(\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}\)
  • Time invariant diff --git a/index.qmd b/index.qmd index 61f1bcd..6d5c2de 100644 --- a/index.qmd +++ b/index.qmd @@ -1041,39 +1041,24 @@ chart = { ###   -:::: {.columns} - -::: {.column width="48%"} - Each day, $t = 1, 2, ... T$ - The **forecaster** receives predictions $\widehat{X}_{t,k}$ from $K$ **experts** - The **forecaster** assigns weights $w_{t,k}$ to each **expert** -- The **forecaster** calculates her prediction: +- The **forecaster** calculates the prediction: + \begin{equation} \widetilde{X}_{t} = \sum_{k=1}^K w_{t,k} \widehat{X}_{t,k}. \label{eq_forecast_def} \end{equation} + - The realization for $t$ is observed -::: + The experts can be institutions, persons, or models -::: {.column width="4%"} + The forecasts can be point-forecasts (i.e., mean or median) or full predictive distributions -::: - -::: {.column width="48%"} - -- 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 a distributional assumption concerning the underlying data -- @cesa2006prediction - -::: - -:::: - ---- + @cesa2006prediction ## The Regret @@ -3005,8 +2990,7 @@ Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. (2023). *Finance Research Lett ### Motivation -Understanding European Allowances (EUA) dynamics is important -for several fields: +Understanding European Emission Allowances (EUA) Portfolio & Risk Management, @@ -3179,7 +3163,8 @@ $$\mathbf{F} = (F_1, \ldots, F_K)^{\intercal}$$ Generalized non-central t-distributions -- Time varying: expectation $\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}$ +- Time varying: + - expectation $\boldsymbol{\mu}_t = (\mu_{1,t}, \ldots, \mu_{K,t})^{\intercal}$ - variance: $\boldsymbol{\sigma}_{t}^2 = (\sigma_{1,t}^2, \ldots, \sigma_{K,t}^2)^{\intercal}$ - Time invariant - degrees of freedom: $\boldsymbol{\nu} = (\nu_1, \ldots, \nu_K)^{\intercal}$