Explanation
Consider a simple time series model y_{t}=d_t+u_{t}\, with u_{t}=\rho u_{t-1}+e_{t}\, where d_t\, is the deterministic part and u_{t}\, is the stochastic part of y_{t}\,. When the true value of \rho \, is close to 1, estimation of the model, i.e. d_t\, will pose efficiency problems because the y_{t}\, will be close to nonstationary. In this setting, testing for the stationarity features of the given times series will also be subject to general statistical problems. To overcome such problems ERS suggested to locally difference the time series. Consider the case where closeness to 1 for the autoregressive parameter is modelled as \rho=1-\frac{c}{T} \, where T \, is the number of observations. Now consider filtering the series using 1-\frac{\bar{c}}{T}L \, with L \, being a standard lag operator, i.e. \bar{y}_t=y_t-(\bar{c}/T)y_{t-1} \,. Working with \bar{y}_t \, would result in power gain, as ERS show, when testing the stationarity features of y_t \, using the augmented Dickey-Fuller test. This is a point optimal test for which \bar{c} \, is set in such a way that the test would have a 50 percent power when the alternative is characterized by \rho=1-c/T \, for c=\bar{c} \,. Depending on the specification of d_t \,, \bar{c} \, will take different values. == References ==