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Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield first-order asymptotics in nonstationary VAR's. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a refinement of central limit theory on function spaces. The theory is used to find asymptotic expansions of the regression coefficients in nonstationary VAR's under very general conditions. The results are specialized to the scalar case and are related to other recent work by the author [21].<\/jats:p>","DOI":"10.1017\/s0266466600004126","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:48:29Z","timestamp":1236685709000},"page":"45-68","source":"Crossref","is-referenced-by-count":36,"title":["Asymptotic Expansions in Nonstationary Vector Autoregressions"],"prefix":"10.1017","volume":"3","author":[{"given":"P. C. 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Cowles Foundation Discussion Paper No. 796, Yale University, July 1986."},{"key":"S0266466600004126_ref020","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/S1573-4412(83)01012-0","volume-title":"Handbook of Econometrics","author":"Phillips","year":"1983"},{"key":"S0266466600004126_ref011","volume-title":"Independent and Stationary Sequences of Random Variables","author":"Ibragimov","year":"1971"},{"key":"S0266466600004126_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6030-1"},{"key":"S0266466600004126_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1911521"},{"key":"S0266466600004126_ref028","volume-title":"Asymptotic Theory for Econometricians","author":"White","year":"1984"},{"key":"S0266466600004126_ref001","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S0266466600004126_ref021","unstructured":"21. Phillips P.C.B. Time series regression with a unit root. Cowles Foundation Discussion Paper No. 740R, Yale University (April 1985), forthcoming in Econometrica, 1986."},{"key":"S0266466600004126_ref015","doi-asserted-by":"publisher","DOI":"10.1137\/0601049"},{"key":"S0266466600004126_ref029","doi-asserted-by":"publisher","DOI":"10.2307\/1911465"},{"key":"S0266466600004126_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.1.91"},{"key":"S0266466600004126_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/1911222"},{"key":"S0266466600004126_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(84)90073-3"},{"key":"S0266466600004126_ref002","volume-title":"Harmonic Analysis and the Theory of Probability","author":"Bochner","year":"1960"},{"key":"S0266466600004126_ref025","first-page":"403","volume-title":"Proceedings of 4th Berkeley Symposium on Mathematical Statistics and Probability","volume":"2","author":"Prohorov","year":"1961"},{"key":"S0266466600004126_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/07474938408800053"},{"key":"S0266466600004126_ref023","unstructured":"23. 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Australian National University (mimeo), 1986."},{"key":"S0266466600004126_ref009","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993379"},{"key":"S0266466600004126_ref006","volume-title":"Generalized Functions","volume":"4","author":"Gelfand","year":"1964"},{"key":"S0266466600004126_ref027","doi-asserted-by":"publisher","DOI":"10.2307\/1912017"},{"key":"S0266466600004126_ref016","doi-asserted-by":"publisher","DOI":"10.2307\/1905674"},{"key":"S0266466600004126_ref014","doi-asserted-by":"crossref","unstructured":"14. Litterman R. B. Forecasting with Bayesian vector autoregressions: Four years of experience. 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