BerriJ/PHD-Presentation
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Not MLE but QMLE

Browse Source
This commit is contained in:
Jonathan Berrisch
2025-06-24 10:11:45 +02:00
parent 1941b43d1c
commit ecff3e485a
2 changed files with 2 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
index.html
View File

@@ -27664,7 +27664,7 @@ Y_{t} = \mu + Y_{t-1} + \varepsilon_t \quad \text{with} \quad \varepsilon_t = \
<li>We draw <span class="math inline">\(2^{12}= 2048\)</span> trajectories 30 steps ahead</li> <li>We draw <span class="math inline">\(2^{12}= 2048\)</span> trajectories 30 steps ahead</li>
</ul> </ul>
<h3 id="estimation">Estimation</h3> <h3 id="estimation">Estimation</h3>
<p>Joint maximum likelihood estimation:</p> <p>Joint (quasi) maximum likelihood estimation:</p>
<p><span class="math display">\[\begin{align*} <p><span class="math display">\[\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}, 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}) \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})

2
index.qmd
View File

@@ -3212,7 +3212,7 @@ $\Lambda(\cdot)$ is a link function:
### Estimation ### Estimation
Joint maximum likelihood estimation: Joint (quasi) maximum likelihood estimation:
\begin{align*} \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}, 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},