{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T18:50:03Z","timestamp":1792695003840,"version":"4.5.0"},"reference-count":46,"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":5673,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1993,8]]},"abstract":"<jats:p>We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(<jats:italic>P<\/jats:italic>) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly identifiable with the error density. We consider a reparameterization of the variance process and show that the identifiable parameters of this process are adaptively estimable.<\/jats:p>","DOI":"10.1017\/s0266466600007970","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:46:44Z","timestamp":1236700004000},"page":"539-569","source":"Crossref","is-referenced-by-count":107,"title":["Adaptive Estimation in ARCH Models"],"prefix":"10.1017","volume":"9","author":[{"given":"Oliver","family":"Linton","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600007970_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/1992480"},{"key":"S0266466600007970_ref017","volume-title":"Nonparametric and Semiparametric Methods in Econometrics and Statistics","author":"Gallant","year":"1991"},{"key":"S0266466600007970_ref001","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345986"},{"key":"S0266466600007970_ref022","first-page":"59","article-title":"On adaptive estimation in autoregressive models when there are nuisance functions","volume":"5","author":"Kreiss","year":"1987","journal-title":"Statistics and Decisions"},{"key":"S0266466600007970_ref027","volume-title":"Asymptotic properties of the quasi-maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models","author":"Lumsdaine","year":"1990"},{"key":"S0266466600007970_ref019","volume-title":"Martingale Limit Theory","author":"Hall","year":"1980"},{"key":"S0266466600007970_ref044","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011397"},{"key":"S0266466600007970_ref030","doi-asserted-by":"publisher","DOI":"10.2307\/2938260"},{"key":"S0266466600007970_ref031","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466600007970_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90064-X"},{"key":"S0266466600007970_ref002","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345863"},{"key":"S0266466600007970_ref020","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350359"},{"key":"S0266466600007970_ref043","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90051-X"},{"key":"S0266466600007970_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532803"},{"key":"S0266466600007970_ref045","volume-title":"Semiparametric ARCH estimation of intra-daily exchange rate volatility","author":"Whistler","year":"1988"},{"key":"S0266466600007970_ref006","article-title":"Quasi-maximum likelihood estimation of dynamic models with time varying covariances","author":"Bollerslev","year":"1991","journal-title":"Econometric Reviews"},{"key":"S0266466600007970_ref003","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1214\/aos\/1176347633","article-title":"Achieving information bounds in non and semiparametric models","volume":"18","author":"Bickel","year":"1990","journal-title":"Annals of Statistics"},{"key":"S0266466600007970_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466600007970_ref024","volume-title":"Festschrift for J. Neyman","author":"Le Cam","year":"1966"},{"key":"S0266466600007970_ref021","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350256"},{"key":"S0266466600007970_ref004","volume-title":"Efficient and Adaptive Inference in Semiparametric Models","author":"Bickel","year":"1991"},{"key":"S0266466600007970_ref033","volume-title":"Conditionally heteroscedastic autoregression","author":"Nemec","year":"1984"},{"key":"S0266466600007970_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90067-2"},{"key":"S0266466600007970_ref013","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1080\/07350015.1991.10509863","article-title":"Semiparametric ARCH models","volume":"9","author":"Engle","year":"1991","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466600007970_ref034","doi-asserted-by":"publisher","DOI":"10.2307\/2938258"},{"key":"S0266466600007970_ref023","first-page":"267","article-title":"Local asymptotically normal families of distributions","volume":"3","author":"Le Cam","year":"1960","journal-title":"University of California Publications in Statistics"},{"key":"S0266466600007970_ref025","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177696960"},{"key":"S0266466600007970_ref012","doi-asserted-by":"publisher","DOI":"10.1080\/07474938608800095"},{"key":"S0266466600007970_ref036","doi-asserted-by":"publisher","DOI":"10.1007\/BF00533249"},{"key":"S0266466600007970_ref042","unstructured":"42. Swensen A.R. Asymptotic inference for a class of stochastic processes. Ph.D. Thesis, Department of Statistics, UC Berkeley (1980)."},{"key":"S0266466600007970_ref028","doi-asserted-by":"publisher","DOI":"10.1086\/294632"},{"key":"S0266466600007970_ref029","first-page":"281","article-title":"The moment structure of ARCH processes","volume":"12","author":"Milhoj","year":"1985","journal-title":"Scandinavian Journal of Statistics"},{"key":"S0266466600007970_ref015","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704476"},{"key":"S0266466600007970_ref032","article-title":"A note on the inequality constraints in the univariate GARCH model","author":"Nelson","year":"1991","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466600007970_ref041","volume-title":"Efficient estimation of models with conditional heteroscedasticity","author":"Steigerwald","year":"1991"},{"key":"S0266466600007970_ref016","article-title":"Local asymptotic minimax and admissibility in estimation","author":"Hajek","year":"1972","journal-title":"Proceedings of the Sixth Berkeley Symposium in Mathematical Statistics"},{"key":"S0266466600007970_ref040","volume-title":"Adaptive estimation in time series regression models","author":"Steigerwald","year":"1990"},{"key":"S0266466600007970_ref026","doi-asserted-by":"publisher","DOI":"10.1007\/BF02532783"},{"key":"S0266466600007970_ref046","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345455"},{"key":"S0266466600007970_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466600007970_ref018","doi-asserted-by":"publisher","DOI":"10.1080\/07474938608800097"},{"key":"S0266466600007970_ref035","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804373"},{"key":"S0266466600007970_ref037","volume-title":"A stationarity condition for the GARCH(1.1) process","author":"Sampson","year":"1988"},{"key":"S0266466600007970_ref039","unstructured":"39. Spanos A. A parametric approach to dynamic heteroscedasticity: The students' t and related linear models. Unpublished manuscript (1990)."},{"key":"S0266466600007970_ref009","volume-title":"Mathematical Methods in Statistics","author":"Cramer","year":"1946"},{"key":"S0266466600007970_ref038","volume-title":"LSE Discussion Paper EM\/90\/220","author":"Shephard","year":"1990"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600007970","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:47:02Z","timestamp":1738993622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600007970\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,8]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,8]]}},"alternative-id":["S0266466600007970"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600007970","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,8]]}}}