{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:38:42Z","timestamp":1779208722937,"version":"3.51.4"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"3-4","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5308,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1994,8]]},"abstract":"<jats:p>This paper proposes a general Bayesian framework for distinguishing between trend- and difference-stationarity. Usually, in model selection, we assume that all of the data were generated by one of the models under consideration. In studying time series, however, we may be concerned that the process is changing over time, so that the preferred model changes over time as well. To handle this possibility, we compute the posterior probabilities of the competing models<jats:italic>for each observation<\/jats:italic>. This way we can see if different segments of the series behave differently with respect to the competing models. The proposed method is a generalization of the usual odds ratio for model discrimination in Bayesian inference. In application, we employ the Gibbs sampler to overcome the computational difficulty. The procedure is illustrated by a real example.<\/jats:p>","DOI":"10.1017\/s0266466600008689","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:43:23Z","timestamp":1236699803000},"page":"596-608","source":"Crossref","is-referenced-by-count":24,"title":["Bayesian Inference of Trend and Difference-Stationarity"],"prefix":"10.1017","volume":"10","author":[{"given":"Robert E.","family":"McCulloch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruey S.","family":"Tsay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008689_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600008689_ref010","volume-title":"Statistical inference of macroeconomic time series via Markov switching models","author":"McCulloch","year":"1992"},{"key":"S0266466600008689_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90093-9"},{"key":"S0266466600008689_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2951602"},{"key":"S0266466600008689_ref007","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1984.4767596"},{"key":"S0266466600008689_ref001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07350015.1993.10509929","article-title":"Bayesian inference of autoregressive time series with mean and variance subject to Markov jumps","volume":"11","author":"Albert","year":"1993","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466600008689_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2347570"},{"key":"S0266466600008689_ref014","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660000877X"},{"key":"S0266466600008689_ref006","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474968"},{"key":"S0266466600008689_ref005","volume-title":"Introduction to Statistical Time Series","author":"Fuller","year":"1976"},{"key":"S0266466600008689_ref013","unstructured":"13. 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