# Detailed calculation of using Augmented Dickey Fuller test in AutoRegressive Model

In the wiki page of ADF test, its testing procedure is applied to the model $$\Delta y_t = \alpha+\beta t+\gamma y_{t-1} + \delta_1 \Delta y_{t-1} + \dots + \delta_{p-1} \Delta y_{t-p+1} + \epsilon_t$$ where $$\alpha$$ is a constant, $$\beta$$ is the coefficient on a time trend and $$p$$ the lag order of the AR process.

Suppose that I want to use ADF test manually to calculate whether the AR(2) process $$y_t = 0.4 + 4y_{t-1} + 6y_{t-2} + \epsilon_t$$ is stationary where $$\epsilon_t$$ is uncorrelated and follows a normal distribution with mean $$0$$ and variance $$3.$$

How should I go about solving this problem?