{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T02:54:24Z","timestamp":1776221664250,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2002,3,6]],"date-time":"2002-03-06T00:00:00Z","timestamp":1015372800000},"content-version":"unspecified","delay-in-days":33,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2002,2]]},"abstract":"<jats:p>Several economic and financial time series are bounded by an \nupper and lower finite limit (e.g., interest rates). It is not \npossible to say that these time series are random walks because \nrandom walks are limitless with probability one (as time goes \nto infinity). Yet, some of these time series behave just like \nrandom walks. In this paper we propose a new approach that takes \ninto account these ideas. We propose a discrete-time and a \ncontinuous-time process (diffusion process) that generate bounded \nrandom walks. These paths are almost indistinguishable from \nrandom walks, although they are stochastically bounded by an \nupper and lower finite limit. We derive for both cases the ergodic \nconditions, and for the diffusion process we present a closed \nexpression for the stationary distribution. This approach suggests \nthat many time series with random walk behavior can in fact \nbe stationarity processes.<\/jats:p>","DOI":"10.1017\/s0266466602181060","type":"journal-article","created":{"date-parts":[[2002,11,14]],"date-time":"2002-11-14T22:01:41Z","timestamp":1037311301000},"page":"99-118","source":"Crossref","is-referenced-by-count":51,"title":["STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS\u2014 THE \nBOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME"],"prefix":"10.1017","volume":"18","author":[{"given":"Jo\u00e3o","family":"Nicolau","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2002,3,6]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602181060","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T19:47:34Z","timestamp":1554580054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602181060\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,2]]}},"alternative-id":["S0266466602181060"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602181060","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,2]]}}}