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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.

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

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