Journal of Economic Literature (JEL) Code(s)
New methods are developed for identifying, estimating and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit root (UR), local unit root (LUR), mildly integrated (MI) and mildly explosive (ME) speciﬁcations in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME speciﬁcations and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the diﬀering forms of house price behavior in Australian state capital cities over the past decade.
Phillips, Peter C. B., "Estimation and Inference with Near Unit Roots" (2021). Cowles Foundation Discussion Papers. 2654.