From b231513d0ac71e7729e9daf58e32111065e491f9 Mon Sep 17 00:00:00 2001 From: Jonathan Berrisch Date: Sun, 22 Jun 2025 10:28:34 +0200 Subject: [PATCH] Remove slide content where possible, improve overview transitions --- index.html | 794 ++++++++++++++++++++++++++--------------------------- index.qmd | 30 +- 2 files changed, 400 insertions(+), 424 deletions(-) diff --git a/index.html b/index.html index 43fba47..94e5392 100644 --- a/index.html +++ b/index.html @@ -25625,10 +25625,8 @@ Risk inherently is a probabilistic concept -
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Overview of the Thesis

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@@ -25687,8 +25685,9 @@ Berrisch, J. (
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Overview of the Thesis

@@ -25747,8 +25746,9 @@ Berrisch, J. (
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Overview of the Thesis

@@ -25807,8 +25807,6 @@ Berrisch, J. (
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Overview

@@ -25826,7 +25824,7 @@ Berrisch, J. (

Reduces estimation time by 2-3 orders of magnitude

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Maintainins competitive forecasting accuracy

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Maintains competitive forecasting accuracy

Real-World Validation in Energy Markets

Python Package ondil on Github and PyPi

@@ -25941,7 +25939,7 @@ Berrisch, J. (
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@@ -26169,7 +26167,7 @@ Berrisch, J. (Each day, \(t = 1, 2, ... T\)

@@ -26571,15 +26571,12 @@ w_{t,k}^{\text{smooth}} = \sum_{l=1}^L \beta_l \varphi_l = \beta'\varphi
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Deviation from best attainable QL (1000 runs).

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CRPS Values for different \(\lambda\) (1000 runs)

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CRPS for different number of knots (1000 runs)

@@ -26587,7 +26584,6 @@ w_{t,k}^{\text{smooth}} = \sum_{l=1}^L \beta_l \varphi_l = \beta'\varphi
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The same simulation carried out for different algorithms (1000 runs):

@@ -26656,7 +26652,7 @@ w_{t,k}^{\text{smooth}} = \sum_{l=1}^L \beta_l \varphi_l = \beta'\varphi
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Tuning paramter grids:

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Tuning parameter grids:

  • Smoothing Penalty: \(\Lambda= \{0\}\cup \{2^x|x\in \{-4,-3.5,\ldots,12\}\}\)
  • Learning Rates: \(\mathcal{E}= \{2^x|x\in \{-1,-0.5,\ldots,9\}\}\)
    • @@ -26857,7 +26853,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

    \[\begin{equation*} \boldsymbol w_{t,k} = \boldsymbol{\psi}^{\text{mv}} \boldsymbol{b}_{t,k} {\boldsymbol{\psi}^{pr}}' \end{equation*}\]

    -

    with parameter matix \(\boldsymbol b_{t,k}\). The latter is estimated to penalize \(L_2\)-smoothing which minimizes

    +

    with parameter matrix \(\boldsymbol b_{t,k}\). The latter is estimated to penalize \(L_2\)-smoothing which minimizes

    \[\begin{align} & \| \boldsymbol{\beta}_{t,d, k}' \boldsymbol{\varphi}^{\text{pr}} - \boldsymbol b_{t, d, k}' \boldsymbol{\psi}^{\text{pr}} \|^2_2 + \lambda^{\text{pr}} \| \mathcal{D}_{q} (\boldsymbol b_{t, d, k}' \boldsymbol{\psi}^{\text{pr}}) \|^2_2 + \nonumber \\ & \| \boldsymbol{\beta}_{t, p, k}' \boldsymbol{\varphi}^{\text{mv}} - \boldsymbol b_{t, p, k}' \boldsymbol{\psi}^{\text{mv}} \|^2_2 + \lambda^{\text{mv}} \| \mathcal{D}_{q} (\boldsymbol b_{t, p, k}' \boldsymbol{\psi}^{\text{mv}}) \|^2_2 \nonumber @@ -27230,7 +27226,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

    - +
    @@ -27238,194 +27234,194 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
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    @@ -27593,7 +27589,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \ F_{\boldsymbol{X}_t|\mathcal{F}_{t-1}}(\boldsymbol{x}_t) = C_{\boldsymbol{U}_{t}|\mathcal{F}_{t - 1}}(\boldsymbol{u}_t) \nonumber \end{align}\]

    with: \(\boldsymbol{u}_t =(u_{1,t},\ldots, u_{K,t})^\intercal\), \(u_{k,t} = F_{X_{k,t}|\mathcal{F}_{t-1}}(x_{k,t})\)

    -

    For brewity we drop the conditioning on \(\mathcal{F}_{t-1}\).

    +

    For brevity we drop the conditioning on \(\mathcal{F}_{t-1}\).

    The model can be specified as follows

    \[\begin{align} F(\boldsymbol{x}_t) = C \left[\mathbf{F}(\boldsymbol{x}_t; \boldsymbol{\mu}_t, \boldsymbol{ \sigma }_{t}^2, \boldsymbol{\nu}, \boldsymbol{\lambda}); \Xi_t, \Theta\right] \nonumber @@ -27662,7 +27658,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

  • We draw \(2^{12}= 2048\) trajectories 30 steps ahead

Estimation

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Joint maximum lieklihood estimation:

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Joint maximum likelihood estimation:

\[\begin{align*} f_{\mathbf{X}_t}(\mathbf{x}_t | \mathcal{F}_{t-1}) = c\left[\mathbf{F}(\mathbf{x}_t;\boldsymbol{\mu}_t, \boldsymbol{\sigma}_{t}^2, \boldsymbol{\nu}, \boldsymbol{\lambda});\Xi_t, \Theta\right] \cdot \\ \prod_{i=1}^K f_{X_{i,t}}(\mathbf{x}_t;\boldsymbol{\mu}_t, \boldsymbol{\sigma}_{t}^2, \boldsymbol{\nu}, \boldsymbol{\lambda}) @@ -27858,7 +27854,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \

  • The cross-sectional dependence is ignored
  • VES models deliver poor performance in short horizons
    • -
  • For Oil prices the RW Benchmark can’t be oupterformed 30 steps ahead
    • +
  • For Oil prices the RW Benchmark can’t be outperformed 30 steps ahead
  • Both VECM models generally deliver good performance
    • @@ -28340,7 +28336,7 @@ Coal

    Accounting for heteroscedasticity or stabilizing the variance via log transformation is crucial for good performance in terms of ES

      -
    • Price dynamics emerged way before the russian invaion into ukraine
      • +
    • Price dynamics emerged way before the Russian invasion into Ukraine
    • Linear dependence between the series reacted only right after the invasion
    • Improvements in forecasting performance is mainly attributed to:
        diff --git a/index.qmd b/index.qmd index 11054b5..61f1bcd 100644 --- a/index.qmd +++ b/index.qmd @@ -173,11 +173,7 @@ col_yellow <- "#FCE135" :::: -## Overview of the Thesis {#sec-overview} - -::: {.r-stack} - -::: {.fragment .fade-in-then-out} +## Overview of the Thesis {#sec-overview transition="fade" transition-speed="slow"} @@ -238,9 +234,7 @@ col_yellow <- "#FCE135"
        -::: - -::: {.fragment .fade-in-then-out} +## Overview of the Thesis {transition="fade" transition-speed="slow" visibility="uncounted"} @@ -301,9 +295,7 @@ col_yellow <- "#FCE135"
        -::: - -::: {.fragment .fade-in-then-out} +## Overview of the Thesis {transition="fade" transition-speed="slow" visibility="uncounted"} @@ -364,9 +356,6 @@ col_yellow <- "#FCE135"
        -::: - -::: ## Overview @@ -1730,8 +1719,7 @@ for( t in 1:T ) {     $\boldsymbol \beta_{t} = K \boldsymbol \beta_{0} \odot \boldsymbol {SoftMax}\left( - \boldsymbol \eta_{t} \odot \boldsymbol R_{t} + \log( \boldsymbol \eta_{t}) \right)$     $\boldsymbol w_{t}(\boldsymbol P) = \underbrace{\boldsymbol B(\boldsymbol B'\boldsymbol B+ \lambda (\alpha \boldsymbol D_1'\boldsymbol D_1 + (1-\alpha) \boldsymbol D_2'\boldsymbol D_2))^{-1} \boldsymbol B'}_{\boldsymbol{\mathcal{H}}} \boldsymbol B \boldsymbol \beta_{t}$ - -} +

        }

        ::: @@ -1775,20 +1763,14 @@ Data Generating Process of the [simple probabilistic example](#simple_example): ## QL Deviation -Deviation from best attainable QL (1000 runs). - -![](assets/crps_learning/pre_vs_post.gif) +![](assets/crps_learning/pre_vs_post.gif) ## CRPS vs. Lambda -CRPS Values for different $\lambda$ (1000 runs) - ![](assets/crps_learning/pre_vs_post_lambda.gif) ## Knots -CRPS for different number of knots (1000 runs) - ![](assets/crps_learning/pre_vs_post_kstep.gif) :::: @@ -1799,8 +1781,6 @@ CRPS for different number of knots (1000 runs) ## Comparison to EWA and ML-Poly -The same simulation carried out for different algorithms (1000 runs): -