{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:21:24Z","timestamp":1776385284076,"version":"3.51.2"},"reference-count":75,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T00:00:00Z","timestamp":1397174400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>In this paper, we provide a survey of Peter Phillips\u2019s works on the econometrics for models with nonstationary nonlinearity, and some of the extensions that were made possible due to his original contributions. Parametric and nonparametric models are considered in both discrete time and continuous time setups. Although some of the asymptotics in the paper are applicable more generally for a wide variety of nonstationary models, we mainly analyze models with nonstationary processes that allow for the functional limit theory with limit processes having well defined local times.<\/jats:p>","DOI":"10.1017\/s0266466613000510","type":"journal-article","created":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T08:51:57Z","timestamp":1397206317000},"page":"894-922","source":"Crossref","is-referenced-by-count":4,"title":["NONSTATIONARY NONLINEARITY: A SURVEY ON PETER PHILLIPS\u2019S CONTRIBUTIONS WITH A NEW PERSPECTIVE"],"prefix":"10.1017","volume":"30","author":[{"given":"Joon Y.","family":"Park","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,4,11]]},"reference":[{"key":"S0266466613000510_ref75","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2011.00361.x"},{"key":"S0266466613000510_ref74","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012032"},{"key":"S0266466613000510_ref73","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOS975"},{"key":"S0266466613000510_ref72","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466610000277"},{"key":"S0266466613000510_ref71","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.3982\/ECTA7732","article-title":"Structural nonparametric cointegrating regression","volume":"77","author":"Wang","year":"2009","journal-title":"Econometrica"},{"key":"S0266466613000510_ref69","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466611000648"},{"key":"S0266466613000510_ref66","volume-title":"Exercises in Econometrics","author":"Phillips","year":"1978"},{"key":"S0266466613000510_ref65","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348666"},{"key":"S0266466613000510_ref64","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00141-6"},{"key":"S0266466613000510_ref29","volume-title":"Independent and Stationary Sequences of Random Variables","author":"Ibragimov","year":"1971"},{"key":"S0266466613000510_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.10.003"},{"key":"S0266466613000510_ref42","unstructured":"Kim J. & Park J.Y. (2013a) Asymptotics for Recurrent Diffusions with Application to High Frequency Regression Working paper, Indiana University."},{"key":"S0266466613000510_ref67","volume-title":"Continuous Martingales and Brownian Motion, 3rd ed","author":"Revuz","year":"2005"},{"key":"S0266466613000510_ref10","volume-title":"Limit Theorems for Functionals of Random Walks","author":"Borodin","year":"1995"},{"key":"S0266466613000510_ref58","doi-asserted-by":"publisher","DOI":"10.1002\/jae.600"},{"key":"S0266466613000510_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604203085"},{"key":"S0266466613000510_ref22","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466613000510_ref53","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00180"},{"key":"S0266466613000510_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00095-7"},{"key":"S0266466613000510_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989938"},{"key":"S0266466613000510_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.016"},{"key":"S0266466613000510_ref27","doi-asserted-by":"publisher","DOI":"10.1002\/jae.747"},{"key":"S0266466613000510_ref48","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466611000119"},{"key":"S0266466613000510_ref38","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001181"},{"key":"S0266466613000510_ref33","unstructured":"Jeong M. & Park J.Y. (2010) Asymptotics for Maximum Likelihood Estimators of Diffusion Models. Working paper, Indiana University."},{"key":"S0266466613000510_ref17","doi-asserted-by":"publisher","DOI":"10.1111\/1368-423X.00054"},{"key":"S0266466613000510_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.01.030"},{"key":"S0266466613000510_ref43","unstructured":"Kim J. & Park J.Y. (2013b) Mean Reversion and Unit Root Properties of Diffusion Models. Working paper, Indiana University."},{"key":"S0266466613000510_ref57","doi-asserted-by":"publisher","DOI":"10.2307\/2171845"},{"key":"S0266466613000510_ref70","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090269"},{"key":"S0266466613000510_ref6","unstructured":"Bandi F.M. & Corradi V. (2011) Nonparametric Nonstationarity Tests. Working paper, University of Warwick."},{"key":"S0266466613000510_ref40","doi-asserted-by":"publisher","DOI":"10.1007\/BF00718037"},{"key":"S0266466613000510_ref61","doi-asserted-by":"publisher","DOI":"10.2307\/2297602"},{"key":"S0266466613000510_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608080365"},{"key":"S0266466613000510_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00208-2"},{"key":"S0266466613000510_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1765(91)90186-O"},{"key":"S0266466613000510_ref2","unstructured":"A\u00eft-Sahalia Y. & Park J.Y. (2013) Bandwidth Selection and Asymptotic Properties of Local Nonparametric Estimators in Possibly Nonstationary Continuous-time Models. Working paper, Indiana University."},{"key":"S0266466613000510_ref49","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00100-8"},{"key":"S0266466613000510_ref46","doi-asserted-by":"publisher","DOI":"10.1214\/154957806100000202"},{"key":"S0266466613000510_ref44","first-page":"165","article-title":"Invariance principles for dependent variables","volume":"32","author":"McLeish","year":"1975","journal-title":"Probability Theory and Related Fields"},{"key":"S0266466613000510_ref34","unstructured":"Jeong M. & Park J.Y. (2013) Asymptotics for Maximum Likelihood Estimators of Jump Diffusion Models. Working paper, Indiana University."},{"key":"S0266466613000510_ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.09.014"},{"key":"S0266466613000510_ref45","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995772"},{"key":"S0266466613000510_ref68","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604202031"},{"key":"S0266466613000510_ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.01.037"},{"key":"S0266466613000510_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00220-8"},{"key":"S0266466613000510_ref56","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.535"},{"key":"S0266466613000510_ref3","first-page":"57","article-title":"Comportement asymptotique du temps d\u2019occupation du processus des sommes partielles","volume":"29","author":"Akonom","year":"1993","journal-title":"Annales de l\u2019Institut Henri Poincar\u00e9"},{"key":"S0266466613000510_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00966355"},{"key":"S0266466613000510_ref7","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00395"},{"key":"S0266466613000510_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-50897-3.50006-7"},{"key":"S0266466613000510_ref9","volume-title":"Statistics for Long-Memory Processes","author":"Beran","year":"1994"},{"key":"S0266466613000510_ref13","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2012.00371.x"},{"key":"S0266466613000510_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.09.032"},{"key":"S0266466613000510_ref16","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2011.520567"},{"key":"S0266466613000510_ref52","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00157"},{"key":"S0266466613000510_ref18","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-937X.2009.00549.x"},{"key":"S0266466613000510_ref63","unstructured":"Phillips P.C.B. & Park J.Y. (1998) Nonstationary density estimation and kernel autoregression. Cowles Foundation Discussion paper 1181."},{"key":"S0266466613000510_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990065"},{"key":"S0266466613000510_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466609990363"},{"key":"S0266466613000510_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS698"},{"key":"S0266466613000510_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.10.004"},{"key":"S0266466613000510_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/009117904000000658"},{"key":"S0266466613000510_ref26","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.07182"},{"key":"S0266466613000510_ref32","unstructured":"Jeganathan P . (2008) Limit Theorems for Functionals of Sums that Converge to Fractional Brownian and Stable Motions. Working paper, Indian Statistical Institute."},{"key":"S0266466613000510_ref36","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660505022X"},{"key":"S0266466613000510_ref37","unstructured":"Kanaya S . (2011) A Nonparametric Test for Stationarity in Continuous-time Markov Processes. Working paper, University of Oxford."},{"key":"S0266466613000510_ref39","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1214\/aos\/1009210546","article-title":"Nonparametric estimation in null recurrent time series","volume":"29","author":"Karlsen","year":"2001","journal-title":"Annals of Statistics"},{"key":"S0266466613000510_ref50","unstructured":"Park J.Y . (2006) Spatial Analysis of Time Series. Working paper, Texas A& M University."},{"key":"S0266466613000510_ref51","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466699153015"},{"key":"S0266466613000510_ref54","doi-asserted-by":"publisher","DOI":"10.2307\/1911875"},{"key":"S0266466613000510_ref55","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466613000510_ref59","doi-asserted-by":"publisher","DOI":"10.1111\/j.1536-7150.2005.00355.x"},{"key":"S0266466613000510_ref60","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466607070260"},{"key":"S0266466613000510_ref62","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.01.017"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466613000510","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,21]],"date-time":"2019-04-21T21:57:39Z","timestamp":1555883859000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466613000510\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,11]]},"references-count":75,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["S0266466613000510"],"URL":"https:\/\/doi.org\/10.1017\/s0266466613000510","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,11]]}}}