A Graphical Procedure for Determining Nonstationarity in Time Series
提出一种基于广义协方差的图形方法，通过绘制原始数据增量的平方均值图，直观判断时间序列所需的差分阶数d，并辅以正式推断检验，帮助研究者避免差分不足或过度的问题。
Abstract Integrated processes as models for time series data have proved to be an important component of the highly flexible class of ARIMA(p, d, q) models. Determining the amount of differencing, d, has been a difficult task: too little and the process is not yet second-order stationary; too much and the process is more variable than it need be. It is shown that by introducing the notion of generalized covariances, developed by Matheron (1973) for spatial processes, the amount of differencing needed can be read easily from a sequence of graphs showing averages of squares of primary data increments. Formal inference to determine if the last difference really is necessary can then be carried out. Time series data are analyzed in this way and compared with the hypothesis-testing approach illustrated by Dickey, Bell, and Miller (1986). Once the order of differencing has been diagnosed, either the differenced time series can be analyzed or the generalized covariance of the undifferenced series can be estimated.