The asymptotic size and power of the augmented Dickey–Fuller test for a unit root
证明增广迪基-富勒检验在单位根原假设下的极限分布适用于比线性自回归过程更广的假设条件，并在备择假设下推导其极限分布，解释检验力随自回归阶数增加而下降的原因。
It is shown that the limiting distribution of the augmented Dickey–Fuller (ADF) test under the null hypothesis of a unit root is valid under a very general set of assumptions that goes far beyond the linear AR(∞) process assumption typically imposed. In essence, all that is required is that the error process driving the random walk possesses a continuous spectral density that is strictly positive. Furthermore, under the same weak assumptions, the limiting distribution of the ADF test is derived under the alternative of stationarity, and a theoretical explanation is given for the well-known empirical fact that the test's power is a decreasing function of the chosen autoregressive order p. The intuitive reason for the reduced power of the ADF test is that, as p tends to infinity, the p regressors become asymptotically collinear.