{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T20:24:41Z","timestamp":1698092681731},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":6647,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1990,12]]},"abstract":"<jats:p>A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and\" test statistics arising from nonstationary and\/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the Fredholm determinant and resolvent of a given kernel. Some examples are also shown to illustrate our methodology.<\/jats:p>","DOI":"10.1017\/s0266466600005430","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:44:48Z","timestamp":1236699888000},"page":"411-432","source":"Crossref","is-referenced-by-count":19,"title":["The Fredholm Approach to Asymptotic Inference on Nonstationary and Noninvertible Time Series Models"],"prefix":"10.1017","volume":"6","author":[{"given":"Katsuto","family":"Tanaka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600005430_ref023","doi-asserted-by":"publisher","DOI":"10.2307\/2938339"},{"key":"S0266466600005430_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.1.91"},{"key":"S0266466600005430_ref027","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177699449"},{"key":"S0266466600005430_ref025","unstructured":"25. 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