Estimation and Inference with Near Unit Roots

Phillips, Peter C.B. (2022) Estimation and Inference with Near Unit Roots. Econometric Theory. (doi:10.1017/S0266466622000342).

Record type: Article

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.

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Accepted/In Press date: 12 June 2022

e-pub ahead of print date: 27 July 2022

Published date: 27 July 2022

Additional Information: Funding Information: Thanks go to the Co-Editor and two referees for helpful comments on the earlier version. The paper is a four-decadal sequel to Phillips (). Some preliminary findings were reported in 2011 in a draft paper with a different title (Phillips, ) that was never completed. The present paper completes that earlier analysis, studies identification issues, formulates a new localizing rate sequence, and provides limit theory, inferential procedures, simulations, and an empirical application. Computations were performed by the author in MATLAB. Support is acknowledged from the NSF under Grant Nos. SES-09 56687 and SES-18 50860, and a Kelly Fellowship at the University of Auckland. Publisher Copyright: © 2022 The Author(s). Published by Cambridge University Press.