Limiting power of unit-root tests in time-series regression
The model considered in this paper is \(y_ t=x'_ t\beta +\eta_ t\), \(\eta_ t=\rho \eta_{t-1}+v_ t\), where \(y_ t\) is scalar, \(x_ t\) is a nonstochastic vector, and the \(v_ t\) are martingale differences satisfying certain moment conditions. To test \(H_ 0: \rho =1\) against \(H_ 1: \rho <1\) or \(H'_ 1: \rho >1\), six different test statistics are considered, all defined as ratios of quadratic forms in \({\hat \eta}{}_ t's\) (residuals from ordinary least squares estimation), or \({\tilde \eta}{}_ t's\) (residuals from generalized least squares estimation). Local alternatives with \(\rho =1-c/T\) (c a constant, T sample size) are studied. The authors conclude that ``the limiting powers of some unit- root tests are computed accurately under a sequence of local alternatives. The limiting powers are found to give a good approximation to the finite-sample powers. An extension of the model is also discussed allowing for autocorrelated errors in the AR(1) process''.
residuals from ordinary least squares estimation
residuals from generalized least squares estimation
scientific article; zbMATH DE number 4190957
scientific article