# Proof for how the drift estimator, for a random walk with drift, is unbiased?

Random walk with drift formula is: (Yt = α + Yt-1 + εt )

How do I go about checking that the drift estimator α-hat is unbiased.. which is proving that E(α-hat) = α?

Is this something I would need strong mathematics background to understand? It seems to be that I cannot find much information about it online.

• Please give out the $\hat \alpha$, otherwise, no one knows biased or unbiased. – user158565 Aug 9 '19 at 1:31
• @user158565 I'm not entirely sure what you mean, I wasn't given a dataset to worth with - just the exact question I'm asking. – dustedcat Aug 9 '19 at 1:39

$$\triangle y_{t} = \alpha + \epsilon_{t}$$
$$E(\triangle y_{t}) = \alpha \rightarrow \hat{\alpha} = \bar{(\triangle y}_{t}) = \frac{\sum_{t=1}^{n}\triangle y_{t}}{n}$$
and it' straightforward to show that $$\hat{\alpha}$$ is unbiased.