{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T16:42:43Z","timestamp":1790613763743,"version":"4.1.0"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T00:00:00Z","timestamp":1162512000000},"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":[[2006,12]]},"abstract":"<jats:p>This paper develops a dynamic switching model, with a random walk and\n                                a stationary regime, where the time spent in the random walk regime\n                                is endogeneously predetermined. More precisely, we assume that the\n                                process is recursively defined by\n                                        <jats:italic>Y<\/jats:italic><jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub> = \u03bc +\n                                    <jats:italic>Y<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>\u22121<\/jats:sub> +\n                                        \u03b5<jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub>, with stochastic probability\n                                        \u03c0<jats:sub>\n\t      <jats:italic>rw<\/jats:italic>\n\t    <\/jats:sub>(<jats:italic>Y<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>\u22121<\/jats:sub>),\n                                    <jats:italic>Y<\/jats:italic><jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub> = \u03bc +\n                                        \u03b5<jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub>, with stochastic probability\n                                1 \u2212\n                                        \u03c0<jats:sub>\n\t      <jats:italic>rw<\/jats:italic>\n\t    <\/jats:sub>(<jats:italic>Y<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>\u22121<\/jats:sub>),\n                                where (\u03b5<jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub>) is a strong white noise and\n                                        \u03c0<jats:sub>\n\t      <jats:italic>rw<\/jats:italic>\n\t    <\/jats:sub> is a nondecreasing function.\n                                Then, the dynamics of the process\n                                        (<jats:italic>Y<\/jats:italic><jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub>), its\n                                marginal distribution, and the distribution of the time spent in the\n                                unit root regime depend on the pattern of random walk intensity\n                                        \u03c0<jats:sub>\n\t      <jats:italic>rw<\/jats:italic>\n\t    <\/jats:sub> and on the noise\n                                distribution <jats:italic>F<\/jats:italic>. Moreover, we study the links\n                                between the endogeneous switching regime and the degree of\n                                persistence of the process\n                                        (<jats:italic>Y<\/jats:italic><jats:sub>\n\t      <jats:italic>t<\/jats:italic>\n\t    <\/jats:sub>).<\/jats:p>","DOI":"10.1017\/s0266466606060518","type":"journal-article","created":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T20:02:27Z","timestamp":1162584147000},"page":"1052-1090","source":"Crossref","is-referenced-by-count":40,"title":["STOCHASTIC UNIT ROOT MODELS"],"prefix":"10.1017","volume":"22","author":[{"given":"Christian","family":"Gourieroux","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian Y.","family":"Robert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2006,11,3]]},"reference":[{"key":"S0266466606060518_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2527284"},{"key":"S0266466606060518_ref001","unstructured":"Asmussen, S. 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(2005) Simple (but effective) Tests of Long Memory versus Structural Breaks. Discussion paper, Queen's University."},{"key":"S0266466606060518_ref027","doi-asserted-by":"crossref","unstructured":"Tong, H. (1990) Non-linear Time Series\u2014A Dynamical System Approach. Oxford University Press.","DOI":"10.1093\/oso\/9780198522249.001.0001"},{"key":"S0266466606060518_ref023","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3267-7"},{"key":"S0266466606060518_ref025","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1995.tb04060.x"},{"key":"S0266466606060518_ref024","unstructured":"Rahbek, A. & N. Shephard (2002) Inference and Ergodicity in the Autoregressive Conditional Root Model. 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