我觉得C是正确的

问题如下：

Question An analyst is investigating whether a time series x_t has a unit root. To implement a Dickey–Fuller test, the analyst must first run a simple linear regression where the dependent variable is the first difference of the time series (x_t – x_t–1) and the independent variable is the:

选项：

A.A.first lag of the time series (x_t–1).

B.B.first lag of the time series minus one (x_t–1 – 1).

C.C.first lag of the first difference of the time series (x_t–1 – x_t–2).

解释：

• A is Correct because, according to the Dickey–Fuller test, if there is a unit root in the AR(1) model (x_t – x_t–1 = b₀ + g₁x_t–1 + ε_t), then g₁ will be 0 in a regression where the dependent variable is the first difference of the time series (x_t – x_t–1) and the independent variable is the first lag of the time series (x_t–1).

• B is Incorrect because, in a Dickey–Fuller test, the independent variable is the first lag of the time series, not the first lag of the time series minus one.

• C is Incorrect because, in a Dickey–Fuller test, the independent variable is the first lag of the time series, not the first lag of the first difference of the time series.