{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T22:23:27Z","timestamp":1649197407498},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T00:00:00Z","timestamp":1337558400000},"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":[[2012,8]]},"abstract":"<jats:p>For many time series in empirical macro and finance, it is assumed that the logarithm of the series is a unit root process. Since we may want to assume a stable growth rate for the macroeconomics time series, it seems natural to potentially model such a series as a unit root process with drift. This assumption implies that the level of such a time series is the exponential of a unit root process with drift and therefore, it is of substantial interest to investigate analytically the behavior of the exponential of a unit root process with drift. This paper shows that the sum of the exponential of a random walk with drift converges in distribution, after rescaling by the exponential of the maximum value of the random walk process. A similar result was established in earlier work for unit root processes without drift. The results derived here suggest the conjecture that also in the case when the Dickey-Fuller test or the KPSS statistic is applied to the exponential of a unit root process with drift, these tests will asymptotically indicate stationarity.<\/jats:p>","DOI":"10.1017\/s026646661100082x","type":"journal-article","created":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T09:56:46Z","timestamp":1337594206000},"page":"915-924","source":"Crossref","is-referenced-by-count":2,"title":["SUMS OF EXPONENTIALS OF RANDOM WALKS WITH DRIFT"],"prefix":"10.1017","volume":"28","author":[{"given":"Xi","family":"Qu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"de Jong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,5,21]]},"reference":[{"key":"S026646661100082X_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994378"},{"key":"S026646661100082X_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(97)00142-0"},{"key":"S026646661100082X_ref9","volume-title":"An Introduction to Probability Theory and its Application","volume":"2","author":"Feller","year":"1968"},{"key":"S026646661100082X_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0084.2008.00531.x"},{"key":"S026646661100082X_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(93)90050-F"},{"key":"S026646661100082X_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603195072"},{"key":"S026646661100082X_ref4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1995.tb00253.x"},{"key":"S026646661100082X_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660000699X"},{"key":"S026646661100082X_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00031-6"},{"key":"S026646661100082X_ref6","unstructured":"de Jong R. (2010) Exponentials of Unit Root Processes. Working paper, Ohio State University."},{"key":"S026646661100082X_ref10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1991.tb00078.x"},{"key":"S026646661100082X_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466699153015"},{"key":"S026646661100082X_ref1","article-title":"Limit theorems for functionals of random walks","volume":"195","author":"Borodin","year":"1995","journal-title":"Proceedings of the Steklov Institute of Mathematics"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646661100082X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T19:10:23Z","timestamp":1556219423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646661100082X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,21]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["S026646661100082X"],"URL":"https:\/\/doi.org\/10.1017\/s026646661100082x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,21]]}}}