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This note considers the effect of changing the quality of the information embodied in a forecast of a conditional variance. Adding noise of a certain form thickens the tails of the normalized errors, but decreasing the amount of information used in the forecast may or may not thicken the tails. We also explore the relation between tail thickness and various notions of \u201coptimal\u201d volatility forecasts. The relationship is surprisingly complicated.<\/jats:p>","DOI":"10.1017\/s0266466600006460","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:39:37Z","timestamp":1236699577000},"page":"113-128","source":"Crossref","is-referenced-by-count":1,"title":["A Note on the Normalized Errors in ARCH and Stochastic Volatility Models"],"prefix":"10.1017","volume":"12","author":[{"given":"Daniel B.","family":"Nelson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"volume-title":"Advances in Futures and Options Research","year":"1993","author":"Engle","key":"S0266466600006460_ref007"},{"volume-title":"Optimal Statistical Decisions","year":"1970","author":"DeGroot","key":"S0266466600006460_ref005"},{"volume-title":"Stochastic Dominance: An Approach to Decision Making under Risk","year":"1978","author":"Whitmore","key":"S0266466600006460_ref023"},{"volume-title":"Dynamic Econometric Modelling","year":"1988","author":"Geweke","key":"S0266466600006460_ref008"},{"key":"S0266466600006460_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(90)90046-3"},{"key":"S0266466600006460_ref015","first-page":"1","volume-title":"Econometrica","volume":"62","author":"Nelson","year":"1994"},{"key":"S0266466600006460_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(94)90043-4"},{"key":"S0266466600006460_ref021","first-page":"107","volume-title":"Econometric Theory 2","author":"Weiss","year":"1986"},{"key":"S0266466600006460_ref004","doi-asserted-by":"crossref","first-page":"2959","DOI":"10.1016\/S1573-4412(05)80018-2","volume-title":"The Handbook of Econometrics","volume":"4","author":"Bollerslev","year":"1994"},{"volume-title":"An Introduction to Bayesian Inference in Econometrics","year":"1971","author":"Zellner","key":"S0266466600006460_ref024"},{"key":"S0266466600006460_ref001","doi-asserted-by":"publisher","DOI":"10.1086\/296451"},{"key":"S0266466600006460_ref002","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.28.6.698"},{"key":"S0266466600006460_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/1925546"},{"key":"S0266466600006460_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466600006460_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1912559"},{"key":"S0266466600006460_ref010","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1080\/07350015.1994.10524553","article-title":"Bayesian analysis of stochastic volatility models","volume":"12","author":"Jacquier","year":"1994","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466600006460_ref011","unstructured":"Lumsdaine R.L. (1994) Asymptotic Properties of the Quasi-Maximum Likelihood Estimator in GARCH(l.l) and IGARCH(l.l) Models. Working paper, Princeton University."},{"key":"S0266466600006460_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90100-8"},{"key":"S0266466600006460_ref014","doi-asserted-by":"publisher","DOI":"10.2307\/2938260"},{"key":"S0266466600006460_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(90)90101-X"},{"key":"S0266466600006460_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(70)90038-4"},{"key":"S0266466600006460_ref019","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1994.tb00057.x"},{"key":"S0266466600006460_ref020","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522249.001.0001","volume-title":"Non-Linear Time Series: A Dynamical System Approach","author":"Tong","year":"1990"},{"key":"S0266466600006460_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1996(93)90003-G"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600006460","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:45:52Z","timestamp":1738993552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600006460\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S0266466600006460"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600006460","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"type":"print","value":"0266-4666"},{"type":"electronic","value":"1469-4360"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}