Gaussian Inference in AR(1) Time Series with or without a Unit Root
This note introduces a simple ﬁrst-diﬀerence-based approach to estimation and inference for the AR(1) model. The estimates have virtually no ﬁnite sample bias, are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coeﬀicient passes through unity with a uniform / n rate of convergence. En route, a useful CLT for sample covariances of linear processes is given, following Phillips and Solo (1992). The approach also has useful extensions to dynamic panels.
Phillips, Peter C.B. and Han, Chirok, "Gaussian Inference in AR(1) Time Series with or without a Unit Root" (2006). Cowles Foundation Discussion Papers. 1834.