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An I(1) or I(2) solution to an autoregressive law of motion is obtained when the inverse of the autoregressive operator pencil has a pole of first or second order at one. We obtain a range of necessary and sufficient conditions for such a pole to be of first or second order. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.<\/jats:p>","DOI":"10.1017\/s0266466619000276","type":"journal-article","created":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T10:41:17Z","timestamp":1574419277000},"page":"773-802","source":"Crossref","is-referenced-by-count":19,"title":["REPRESENTATION OF I(1) AND I(2) AUTOREGRESSIVE HILBERTIAN PROCESSES"],"prefix":"10.1017","volume":"36","author":[{"given":"Brendan K.","family":"Beare","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Won-Ki","family":"Seo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2019,11,22]]},"reference":[{"key":"S0266466619000276_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(81)90079-8"},{"key":"S0266466619000276_ref44","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012287"},{"key":"S0266466619000276_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/1913236"},{"key":"S0266466619000276_ref50","unstructured":"Phillips, P.C.B. & Kheifets, I. 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