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ESTIMATION AND INFERENCE WITH NEAR UNIT ROOTS

Published online by Cambridge University Press:  27 July 2022

Peter C.B. Phillips
Peter C.B. Phillips*
Affiliation:
Yale University, University of Auckland, Singapore Management University, and University of Southampton
*
Address correspondence to Peter C. B. Phillips, Cowles Foundation, Yale University, New Haven, CT, USA; e-mail: peter.phillips@yale.edu.
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Abstract

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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.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 2 , April 2023 , pp. 221 - 263
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

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 (1987a). Some preliminary findings were reported in 2011 in a draft paper with a different title (Phillips, 2011) 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.

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