{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T02:41:10Z","timestamp":1782441670326,"version":"3.54.5"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T00:00:00Z","timestamp":1623196800000},"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":[[2022,6]]},"abstract":"<jats:p>Because the ARMA\u2013GARCH model can generate data with some important properties such as skewness, heavy tails, and volatility persistence, it has become a benchmark model in analyzing financial and economic data. The commonly employed quasi maximum likelihood estimation (QMLE) requires a finite fourth moment for both errors and the sequence itself to ensure a normal limit. The self-weighted quasi maximum exponential likelihood estimation (SWQMELE) reduces the moment constraints by assuming that the errors and their absolute values have median zero and mean one, respectively. Therefore, it is necessary to test zero median of errors before applying the SWQMELE, as changing zero mean to zero median destroys the ARMA\u2013GARCH structure. This paper develops an efficient empirical likelihood test without estimating the GARCH model but using the GARCH structure to reduce the moment effect. A simulation study confirms the effectiveness of the proposed test. The data analysis shows that some financial returns do not have zero median of errors, which cautions the use of the SWQMELE. \n<\/jats:p>","DOI":"10.1017\/s0266466621000244","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T15:43:44Z","timestamp":1623253424000},"page":"536-561","source":"Crossref","is-referenced-by-count":7,"title":["TEST FOR ZERO MEDIAN OF ERRORS IN AN ARMA\u2013GARCH MODEL"],"prefix":"10.1017","volume":"38","author":[{"given":"Yaolan","family":"Ma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mo","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Peng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rongmao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"S0266466621000244_r6","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466621000244_r12","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343247"},{"key":"S0266466621000244_r7","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2013.840239"},{"key":"S0266466621000244_r8","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1093265632"},{"key":"S0266466621000244_r14","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-010-0051-9"},{"key":"S0266466621000244_r16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603192092"},{"key":"S0266466621000244_r13","first-page":"425","article-title":"Unified inference for an AR process with possible infinite variance GARCH errors","volume":"18","author":"Huang","year":"2020","journal-title":"Journal of Financial Econometrics"},{"key":"S0266466621000244_r20","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325370"},{"key":"S0266466621000244_r5","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-011-0264-0"},{"key":"S0266466621000244_r10","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00396"},{"key":"S0266466621000244_r17","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1015957401"},{"key":"S0266466621000244_r19","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/90.4.967"},{"key":"S0266466621000244_r1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(01)00156-9"},{"key":"S0266466621000244_r2","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603194030"},{"key":"S0266466621000244_r21","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2016.1224024"},{"key":"S0266466621000244_r24","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.977386"},{"key":"S0266466621000244_r11","first-page":"3442","article-title":"Inference for conditional value-at-risk of a predictive regression","volume":"8","author":"He","year":"2020","journal-title":"Annals of Statistics"},{"key":"S0266466621000244_r18","volume-title":"Empirical Likelihood","author":"Owen","year":"2001"},{"key":"S0266466621000244_r22","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466614000632"},{"key":"S0266466621000244_r3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466621000244_r9","volume-title":"Martingale Limit Theory and Its Application","author":"Hall","year":"1980"},{"key":"S0266466621000244_r4","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060208"},{"key":"S0266466621000244_r23","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS895"},{"key":"S0266466621000244_r15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.07.016"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466621000244","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T13:39:18Z","timestamp":1654868358000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466621000244\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,9]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["S0266466621000244"],"URL":"https:\/\/doi.org\/10.1017\/s0266466621000244","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,9]]}}}