# SER of Random Walk Model?

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, 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.

• If this is a random walk, you errors are iid. You expend one degree of freedeom on $\beta_0$ and that is it. Apr 27, 2021 at 17:22
• In that case $SE(\hat{\beta}_0) = \frac{\hat{\sigma_u}}{\sqrt{n-1}}$ then, as per the linked paper? Apr 27, 2021 at 17:44