Estimation and Inference with Near Unit Roots

Peter Phillips

No 2304, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Cauchy limit distribution; Local to unity; Localizing rate sequence; Mild integration; Mildly explosive process; Unit root (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2021-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Econometric Theory First View, (July, 2022): 1-43.

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