{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T02:52:15Z","timestamp":1776480735078,"version":"3.51.2"},"reference-count":55,"publisher":"The Econometric Society","issue":"4","funder":[{"DOI":"10.13039\/100000077","name":"Division of Social and Economic Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000077","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004853","name":"The Chinese University of Hong Kong, Shenzhen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>We introduce a generalization of the popular local\u2010to\u2010unity model of time series persistence by allowing for<jats:italic>p<\/jats:italic>autoregressive (AR) roots and<jats:italic>p<\/jats:italic>\u2009\u2212\u20091 moving average (MA) roots close to unity. This generalized local\u2010to\u2010unity model, GLTU(<jats:italic>p<\/jats:italic>), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(<jats:italic>p<\/jats:italic>,<jats:italic>p<\/jats:italic>\u2009\u2212\u20091) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited\u2010information Bayesian framework for inference in the GLTU(<jats:italic>p<\/jats:italic>) model and apply it to quantify the uncertainty about the half\u2010life of deviations from purchasing power parity.<\/jats:p>","DOI":"10.3982\/ecta17944","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:50:20Z","timestamp":1626436220000},"page":"1825-1854","source":"Crossref","is-referenced-by-count":7,"title":["Generalized Local\u2010to\u2010Unity Models"],"prefix":"10.3982","volume":"89","author":[{"given":"Liyu","family":"Dou","sequence":"first","affiliation":[{"name":"School of Management and Economics and Shenzhen Finance Institute, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ulrich K.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"key":"ecta300314-bib-0001","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1080\/07350015.1994.10510007","volume":"12","author":"Andrews","year":"1994","journal-title":"Journal of Business and Economic Statistics"},{"key":"ecta300314-bib-0002","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1017\/S0266466600011269","volume":"1","author":"Bergstrom","year":"1985","journal-title":"Econometric Theory"},{"key":"ecta300314-bib-0003","unstructured":"Bobkoski, M. 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