Does the Dickey-Fuller test for a Random Walk?

Is it valid to say that the Dickey-Fuller test, tests for a random walk?

Since the AR(1) process $Y_{t} = \rho Y_{t-1} + e_{t}$ with $\rho = 1$ is the same as the random walk. (Next value is maximum correlated with the previous since $\rho = 1$ + the unpredicted term.

And as wikipedia says, a unit root is present if $\rho = 1$. The model is non-stationary, which we know random walks are.

The reason for asking this is that it feels like an easy way of explaining it and intuitive.

• the short answer is Yes. Most people use augmented DF (ADF) test though. Also, look at the different settings such as trend stationarity – Aksakal Jul 15 '15 at 16:56

This was one of the criticisms towards these tests, since they "break from tradition": if we "suspect" the existence of a unit root ($\rho =1$ instead of, say, $\rho =0.99$), then the established approach would be to set as the null hypothesis the "trend-stationarity" hypothesis, and then attempt to reject it at the conventional significance levels (the latter reflecting an attempt to "preserve" the null, by keeping the Type I error low, i.e. by keeping low the probability of false rejection of the null).