{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T11:37:30Z","timestamp":1791891450196,"version":"4.3.4"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":8966,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econ Theory"],"published-print":{"date-parts":[[1986,4]]},"abstract":"<jats:p>In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.<\/jats:p>","DOI":"10.1017\/s0266466600011397","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:14:39Z","timestamp":1287393279000},"page":"107-131","source":"Crossref","is-referenced-by-count":347,"title":["Asymptotic Theory for ARCH Models: Estimation and Testing"],"prefix":"10.1017","volume":"2","author":[{"given":"Andrew A.","family":"Weiss","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600011397_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BF02613866"},{"key":"S0266466600011397_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/1911465"},{"key":"S0266466600011397_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1911990"},{"key":"S0266466600011397_ref020","unstructured":". Weiss, A. A. Asymptotic theory for ARCH models: Estimation and testing. Mimeograph, Department of Economics, University of Southern California (1984)."},{"key":"S0266466600011397_ref001","first-page":"259","article-title":"Asymptotic properties of maximum likelihood estimators for stochastic processes","volume":"38","author":"Basawa","year":"1976","journal-title":"Sankhya"},{"key":"S0266466600011397_ref013","unstructured":". Milhoj, A. The moment structure of ARCH processes. Research Report No. 94, Institute of Statistics, University of Copenhagen (1984)."},{"key":"S0266466600011397_ref016","first-page":"297","article-title":"The strong consistency of maximum likelihood estimates for ARMA processes","volume":"1","author":"Rissanen","year":"1979","journal-title":"The Annals of Statistics"},{"key":"S0266466600011397_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1912529"},{"key":"S0266466600011397_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1912526"},{"key":"S0266466600011397_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2525707"},{"key":"S0266466600011397_ref017","volume-title":"The estimation of the dynamic regression model with stochastic coefficients","author":"Weiss","year":"1982"},{"key":"S0266466600011397_ref018","unstructured":". Weiss, A. A. Time series models with varying coefficients and variances. Unpublished Ph.D. Thesis, University of Sydney (1983)."},{"key":"S0266466600011397_ref002","first-page":"653","article-title":"Estimation and inference in non-linear structural models","volume":"3","author":"Berndt","year":"1974","journal-title":"Annals of Economic and Social Measurement"},{"key":"S0266466600011397_ref014","volume-title":"Random Coefficient Autoregressive Models","author":"Nicholls","year":"1983"},{"key":"S0266466600011397_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1913829"},{"key":"S0266466600011397_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466600011397_ref011","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316429"},{"key":"S0266466600011397_ref019","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1984.tb00382.x"},{"key":"S0266466600011397_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/2297762"},{"key":"S0266466600011397_ref009","volume-title":"Generating mechanisms, models and causality","author":"Granger","year":"1980"},{"key":"S0266466600011397_ref006","first-page":"293","volume-title":"Proceedings of the ASA-Census-NBER Conference on Applied Time Series Analysis","author":"Engle","year":"1983"},{"key":"S0266466600011397_ref010","unstructured":". Granger, C.W.J. and Robins., R. P. Bivariate time series modelling with forecastable error variances. University of California, San Diego Department of Economics Discussion Paper 82\u201314 (1982)."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600011397","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T05:01:13Z","timestamp":1636434073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600011397\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,4]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,4]]}},"alternative-id":["S0266466600011397"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600011397","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,4]]}}}