Dickey–Fuller test

In statistics, the Dickey–Fuller test tests the null hypothesis of whether a unit root is present in an autoregressive model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is named after the statisticians David Dickey and Wayne Fuller, who developed the test in 1979.

A simple AR(1) model is

where ${\displaystyle y_{t}}$ is the variable of interest, ${\displaystyle t}$ is the time index, ${\displaystyle \rho }$ is a coefficient, and ${\displaystyle u_{t}}$ is the error term. A unit root is present if ${\displaystyle \rho =1}$. The model would be non-stationary in this case.

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