{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T10:14:12Z","timestamp":1788603252852,"version":"build-2803163510"},"reference-count":41,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1017\/s0266466622000342","type":"journal-article","created":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T07:16:33Z","timestamp":1658906193000},"page":"221-263","source":"Crossref","is-referenced-by-count":29,"title":["ESTIMATION AND INFERENCE WITH NEAR UNIT ROOTS"],"prefix":"10.1017","volume":"39","author":[{"given":"Peter C.B.","family":"Phillips","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2022,7,27]]},"reference":[{"key":"S0266466622000342_r10","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/41.1-2.261"},{"key":"S0266466622000342_r15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00798.x"},{"key":"S0266466622000342_r33","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1111\/j.1468-2354.2010.00625.x","article-title":"Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values?","volume":"52","author":"Phillips","year":"2011","journal-title":"International Economic Review"},{"key":"S0266466622000342_r36","doi-asserted-by":"publisher","DOI":"10.1111\/joes.12430"},{"key":"S0266466622000342_r30","doi-asserted-by":"publisher","DOI":"10.1111\/iere.12132"},{"key":"S0266466622000342_r13","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.jeconom.2020.04.038","article-title":"Robust inference for spurious regressions and cointegrations involving processes moderately deviated from a unit root","volume":"219","author":"Lin","year":"2020","journal-title":"Journal of Econometrics"},{"key":"S0266466622000342_r37","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719017","volume-title":"Empirical Processes with Applications to Statistics","author":"Shorack","year":"2009"},{"key":"S0266466622000342_r12","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhu139"},{"key":"S0266466622000342_r35","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.2307\/1910999","article-title":"Approximation to the finite sample distribution for nonstable first order stochastic difference equations","volume":"52","author":"Satchell","year":"1984","journal-title":"Econometrica"},{"key":"S0266466622000342_r22","unstructured":"Phillips, P.C.B. 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(1979) Normalizing transformation for the serial correlation coefficient $\\widehat{\\alpha}$ . 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(2009) Econometric Inference in the Vicinity of Unity. 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