{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:21:23Z","timestamp":1789719683570,"version":"4.0.1"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,11,3]],"date-time":"2014-11-03T00:00:00Z","timestamp":1414972800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p>It is well known that the least squares estimator (LSE) of an AR(<jats:italic>p<\/jats:italic>) model with i.i.d. (independent and identically distributed) noises is<jats:italic>n<\/jats:italic><jats:sup>1\/<\/jats:sup><jats:sup><jats:italic>\u03b1<\/jats:italic><\/jats:sup><jats:italic>L<\/jats:italic>(<jats:italic>n<\/jats:italic>)-consistent when the tail index<jats:italic>\u03b1<\/jats:italic>of the noise is within (0,2) and is<jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup>-consistent when<jats:italic>\u03b1<\/jats:italic>\u2265 2, where<jats:italic>L<\/jats:italic>(<jats:italic>n<\/jats:italic>) is a slowly varying function. When the noises are not i.i.d., however, the case is far from clear. This paper studies the LSE of AR(<jats:italic>p<\/jats:italic>) models with heavy-tailed G-GARCH(1,1) noises. When the tail index<jats:italic>\u03b1<\/jats:italic>of G-GARCH is within (0,2), it is shown that the LSE is not a consistent estimator of the parameters, but converges to a ratio of stable vectors. When<jats:italic>\u03b1<\/jats:italic>\u03b5 [2,4], it is shown that the LSE is<jats:italic>n<\/jats:italic><jats:sup>1\u20132\/<\/jats:sup><jats:sup><jats:italic>\u03b1<\/jats:italic><\/jats:sup>-consistent if<jats:italic>\u03b1<\/jats:italic>\u03b5 (2,4), log<jats:italic>n<\/jats:italic>-consistent if<jats:italic>\u03b1<\/jats:italic>= 2, and<jats:italic>n<\/jats:italic><jats:sup>1\/2<\/jats:sup>\/ log<jats:italic>n<\/jats:italic>-consistent if<jats:italic>\u03b1<\/jats:italic>= 4, and its limiting distribution is a functional of stable processes. Our results are significantly different from those with i.i.d. noises and should warn practitioners in economics and finance of the implications, including inconsistency, of heavy-tailed errors in the presence of conditional heterogeneity.<\/jats:p>","DOI":"10.1017\/s0266466614000632","type":"journal-article","created":{"date-parts":[[2014,11,3]],"date-time":"2014-11-03T10:57:16Z","timestamp":1415012236000},"page":"880-890","source":"Crossref","is-referenced-by-count":42,"title":["ASYMPTOTIC INFERENCE FOR AR MODELS WITH HEAVY-TAILED G-GARCH 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