Answer: A first lag of the time series (\(x_{t-1}\)).

## Explanation For the Dickey-Fuller test, the regression specification is: \[ \Delta x_t = \gamma x_{t-1} + \varepsilon_t \] Where: - \( \Delta x_t = x_t - x_{t-1} \) (first difference, dependent variable) - \( x_{t-1} \) (first lag of the time series, independent variable) **Key points:** - The Dickey-Fuller test examines whether \( \gamma = 0 \) in this regression - If \( \gamma = 0 \), then \( x_t = x_{t-1} + \varepsilon_t \), which is a random walk (unit root) - If \( \gamma < 0 \), the series is stationary **Why option A is correct:** - The independent variable is simply the first lag \( x_{t-1} \) - No transformation like subtracting 1 is needed - The test directly examines the coefficient on the lagged level **Why other options are incorrect:** - Option B: No need to subtract 1 from the lagged variable - Option C: This would be testing for higher-order unit roots, not the basic Dickey-Fuller test

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