{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T05:46:05Z","timestamp":1791524765918,"version":"4.3.4"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5795,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1993,4]]},"abstract":"<jats:p>The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly specified cointegrated Gaussian system, this can be done in a very convenient way. Combining the results of this paper with available general maximum likelihood estimation theories readily shows that the maximum likelihood estimator is asymptotically optimal with a mixed normal limiting distribution. The usefulness of this approach is demonstrated by analyzing a regression model with autoregressive moving average errors and strictly exogenous regressors which may be either integrated of order one, asymptotically stationary, or nonstochastic and bounded.<\/jats:p>","DOI":"10.1017\/s0266466600007490","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:47:46Z","timestamp":1236700066000},"page":"155-188","source":"Crossref","is-referenced-by-count":12,"title":["Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model"],"prefix":"10.1017","volume":"9","author":[{"given":"Pentti","family":"Saikkonen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600007490_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2297545"},{"key":"S0266466600007490_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012287"},{"key":"S0266466600007490_ref006","volume-title":"Real Analysis and Probability","author":"Dudley","year":"1989"},{"key":"S0266466600007490_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/2938179"},{"key":"S0266466600007490_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(88)90039-5"},{"key":"S0266466600007490_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5254-2"},{"key":"S0266466600007490_ref022","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1986.tb00491.x"},{"key":"S0266466600007490_ref019","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348666"},{"key":"S0266466600007490_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012780"},{"key":"S0266466600007490_ref026","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(83)90023-6"},{"key":"S0266466600007490_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350711"},{"key":"S0266466600007490_ref020","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/58.2.299"},{"key":"S0266466600007490_ref005","doi-asserted-by":"publisher","DOI":"10.1080\/00949657708810151"},{"key":"S0266466600007490_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/2938278"},{"key":"S0266466600007490_ref015","doi-asserted-by":"publisher","DOI":"10.1017\/S026646660001344X"},{"key":"S0266466600007490_ref009","volume-title":"Convergence to stochastic integrals of general form. 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