{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T05:02:17Z","timestamp":1768885337753,"version":"3.49.0"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"05","license":[{"start":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T00:00:00Z","timestamp":1542844800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p>This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.<\/jats:p>","DOI":"10.1017\/s0266466618000348","type":"journal-article","created":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T06:41:25Z","timestamp":1542868885000},"page":"943-977","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["STATISTICAL INFERENCE FOR MEASUREMENT EQUATION SELECTION IN THE LOG-REALGARCH MODEL"],"prefix":"10.1017","volume":"35","author":[{"given":"Yu-Ning","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caiya","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2018,11,23]]},"reference":[{"key":"S0266466618000348_ref18","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1234"},{"key":"S0266466618000348_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090129"},{"key":"S0266466618000348_ref16","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2014.897954"},{"key":"S0266466618000348_ref15","doi-asserted-by":"publisher","DOI":"10.1093\/jjfinec\/nbt023"},{"key":"S0266466618000348_ref9","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"S0266466618000348_ref14","doi-asserted-by":"publisher","DOI":"10.1080\/07474938608800097"},{"key":"S0266466618000348_ref8","first-page":"174","volume":"7","year":"2009","journal-title":"Journal of Financial Econometrics"},{"key":"S0266466618000348_ref13","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1093265632"},{"key":"S0266466618000348_ref7","volume-title":"Time Series: Theory and Methods","year":"2009"},{"key":"S0266466618000348_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.05.004"},{"key":"S0266466618000348_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/1913827"},{"key":"S0266466618000348_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90067-2"},{"key":"S0266466618000348_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2016.09.010"},{"key":"S0266466618000348_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"S0266466618000348_ref10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1993.tb05127.x"},{"key":"S0266466618000348_ref4","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/62.1.121"},{"key":"S0266466618000348_ref3","volume-title":"Probability and Measure","year":"1995"},{"key":"S0266466618000348_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00336"},{"key":"S0266466618000348_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.11.001"},{"key":"S0266466618000348_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2015.12.005"},{"key":"S0266466618000348_ref28","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000803"},{"key":"S0266466618000348_ref27","volume-title":"Estimation in Conditionally Heteroscedastic Time Series Model","volume":"181","year":"2005"},{"key":"S0266466618000348_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/07474938608800099"},{"key":"S0266466618000348_ref25","doi-asserted-by":"publisher","DOI":"10.2307\/2938260"},{"key":"S0266466618000348_ref24","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1983.tb00373.x"},{"key":"S0266466618000348_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00096-9"},{"key":"S0266466618000348_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600008215"},{"key":"S0266466618000348_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2015.10.018"},{"key":"S0266466618000348_ref17","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2015.1038543"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466618000348","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T10:10:52Z","timestamp":1568196652000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466618000348\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,23]]},"references-count":29,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["S0266466618000348"],"URL":"https:\/\/doi.org\/10.1017\/s0266466618000348","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,23]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2018\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}