{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T22:35:21Z","timestamp":1770503721457,"version":"3.49.0"},"reference-count":45,"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":4393,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1997,2]]},"abstract":"<jats:p>We develop order<jats:italic>T<\/jats:italic><jats:sup>\u22121<\/jats:sup>asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two-step approximate QMLE in the GARCH(l,l) model. We calculate the approximate mean and skewness and, hence, the Edgeworth-B distribution function. We suggest several methods of bias reduction based on these approximations.<\/jats:p>","DOI":"10.1017\/s0266466600006009","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:35:15Z","timestamp":1236699315000},"page":"558-581","source":"Crossref","is-referenced-by-count":26,"title":["An Asymptotic Expansion in the GARCH(l, 1) Model"],"prefix":"10.1017","volume":"13","author":[{"given":"Oliver","family":"Linton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600006009_ref045","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011397"},{"key":"S0266466600006009_ref044","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004928"},{"key":"S0266466600006009_ref041","first-page":"379","volume-title":"Sankha","volume":"31","author":"Shenton","year":"1969"},{"key":"S0266466600006009_ref040","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1111\/j.2517-6161.1963.tb00511.x","article-title":"Higher moments of a maximum-likelihood estimate","volume":"25","author":"Shenton","year":"1963","journal-title":"Journal of the Royal Statistical Society B"},{"key":"S0266466600006009_ref039","doi-asserted-by":"publisher","DOI":"10.2307\/1913972"},{"key":"S0266466600006009_ref043","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3154-7"},{"key":"S0266466600006009_ref038","first-page":"169","volume-title":"Econometrica","volume":"42","author":"Sargan","year":"1974"},{"key":"S0266466600006009_ref037","doi-asserted-by":"publisher","DOI":"10.2307\/1911356"},{"key":"S0266466600006009_ref036","volume-title":"The Handbook of Econometrics","volume":"II","author":"Rothenberg","year":"1986"},{"key":"S0266466600006009_ref035","doi-asserted-by":"publisher","DOI":"10.2307\/1911186"},{"key":"S0266466600006009_ref033","doi-asserted-by":"publisher","DOI":"10.2307\/1912705"},{"key":"S0266466600006009_ref032","doi-asserted-by":"publisher","DOI":"10.2307\/1912315"},{"key":"S0266466600006009_ref031","doi-asserted-by":"publisher","DOI":"10.2307\/1911222"},{"key":"S0266466600006009_ref030","volume-title":"Developments in Statistics","volume":"3","author":"Pfanzagl","year":"1980"},{"key":"S0266466600006009_ref029","doi-asserted-by":"publisher","DOI":"10.2307\/2938260"},{"key":"S0266466600006009_ref028","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466600006009_ref026","doi-asserted-by":"publisher","DOI":"10.1007\/BF00994269"},{"key":"S0266466600006009_ref023","unstructured":"Lumsdaine R.L. 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