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Second, we consider a rather general specification of shifts and outliers with random size, number, and timing and with flexible dynamics. It nests the classical cases of additive shifts, innovational outliers, and additive outliers. Third, as an instrument for this analysis we develop an asymptotic theory for product moment matrices of linear processes with stochastic level-shift components, generalizing results of Leipus and Viano (2003,<jats:italic>Statistics and Probability Letters<\/jats:italic>61, 177\u2013190).<\/jats:p>","DOI":"10.1017\/s0266466608080249","type":"journal-article","created":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T10:15:42Z","timestamp":1200996942000},"page":"587-615","source":"Crossref","is-referenced-by-count":5,"title":["ASYMPTOTICS FOR COINTEGRATED PROCESSES WITH INFREQUENT STOCHASTIC LEVEL SHIFTS AND OUTLIERS"],"prefix":"10.1017","volume":"24","author":[{"given":"Iliyan","family":"Georgiev","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,1,22]]},"reference":[{"key":"S0266466608080249_ref023","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600165077"},{"key":"S0266466608080249_ref024","doi-asserted-by":"publisher","DOI":"10.1162\/003465397556791"},{"key":"S0266466608080249_ref020","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176990334"},{"key":"S0266466608080249_ref019","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1080\/07350015.1998.10524780","article-title":"A structured VAR for Denmark under changing monetary regimes","volume":"16","author":"Juselius","year":"1998","journal-title":"Journal of Business \u2019 Economic Statistics"},{"key":"S0266466608080249_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012561"},{"key":"S0266466608080249_ref028","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/07350015.1990.10509786","article-title":"Testing for a unit root in a time series with a changing mean","volume":"8","author":"Perron","year":"1990","journal-title":"Journal of Business \u2019 Economic Statistics"},{"volume-title":"Likelihood-Based Inference in Cointegrated Vector Autoregressive Models","year":"1996","author":"Johansen","key":"S0266466608080249_ref017"},{"key":"S0266466608080249_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05265-5"},{"key":"S0266466608080249_ref013","unstructured":"Ibragimov R. \u2019 Phillips P.C.B. (2004) Regression Asymptotics Using Martingale Convergence Methods. 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(2004) An Analytical Evaluation of the Log-Periodogram Estimate in the Presence of Level Shifts and Its Implications for Stock Returns Volatility. 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