<p>Given the following random walk model <span class="math-container">$\Delta Y_t = Y_t - Y_{t-1}=\beta_0+u_t$</span>, where <span class="math-container">$u_t \sim N(0,\sigma^2_u)$</span>, how do we derive the standard error <span class="math-container">$\beta_0$</span> in terms of the estimated <span class="math-container">$\sigma^2_u$</span>? The model is largely similar to the one given <a href="https://www.longevitas.co.uk/site/downloads/RWwD_Note.pdf" rel="nofollow noreferrer">here</a>, except that <span class="math-container">$t=1,2...,T$</span> and <span class="math-container">$Y_0$</span> is a given. I am unsure of how the degrees of freedom might change in this case.</p>

CC BY-SA 4.0
2021-04-27T17:22:38.703Z
If this is a random walk, you errors are iid. You expend one degree of freedeom on $\beta_0$ and that is it.
Grada Gukovic
CC BY-SA 4.0
2021-04-27T17:44:53.770Z
In that case $SE(\hat{\beta}_0) = \frac{\hat{\sigma_u}}{\sqrt{n-1}}$ then, as per the linked paper?
kékszajkók
<econometrics>
SER of Random Walk Model?
kékszajkók
# SER of Random Walk Model?

(Asked by: username_0 on 2021-04-27)

Given the following random walk model $\Delta Y\_t = Y\_t - Y\_{t-1}=\beta\_0+u\_t$, where $u\_t \sim N(0,\sigma^2\_u)$, how do we derive the standard error $\beta\_0$ in terms of the estimated $\sigma^2\_u$? The model is largely similar to the one given [here](https://www.longevitas.co.uk/site/downloads/RWwD_Note.pdf), except that $t=1,2...,T$ and $Y\_0$ is a given. I am unsure of how the degrees of freedom might change in this case.

**Tags:** econometrics
> **Comments:**
> **username_1**: If this is a random walk, you errors are iid. You expend one degree of freedeom on $\beta_0$ and that is it.  
> **username_0**: In that case $SE(\hat{\beta}_0) = \frac{\hat{\sigma_u}}{\sqrt{n-1}}$ then, as per the linked paper?  

---

## 0 answers

