{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:46:16Z","timestamp":1790901976001,"version":"4.1.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2002,3,6]],"date-time":"2002-03-06T00:00:00Z","timestamp":1015372800000},"content-version":"unspecified","delay-in-days":33,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2002,2]]},"abstract":"<jats:p>\n                    This paper first provides some useful results on a generalized \nrandom coefficient autoregressive model and a generalized hidden \nMarkov model. These results simultaneously imply strict \nstationarity, existence of higher order moments, geometric \nergodicity, and \u03b2-mixing with exponential decay rates, which are \nimportant properties for statistical inference. As applications, we \nthen provide easy-to-verify sufficient conditions to ensure \u03b2-mixing \nand finite higher order moments for various linear and nonlinear \nGARCH(1,1), linear and power GARCH(\n                    <jats:italic>p<\/jats:italic>\n                    ,\n                    <jats:italic>q<\/jats:italic>\n                    ), stochastic \nvolatility, and autoregressive conditional duration models. For many of \nthese models, our sufficient conditions for existence of second \nmoments and exponential \u03b2-mixing are also necessary. For several \nGARCH(1,1) models, our sufficient conditions for existence of higher \norder moments again coincide with the necessary ones in He and Terasvirta \n(1999,\n                    <jats:italic>Journal of Econometrics<\/jats:italic>\n                    92, 173\u2013192).\n                  <\/jats:p>","DOI":"10.1017\/s0266466602181023","type":"journal-article","created":{"date-parts":[[2002,11,14]],"date-time":"2002-11-14T17:01:41Z","timestamp":1037293301000},"page":"17-39","source":"Crossref","is-referenced-by-count":425,"title":["MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC \nVOLATILITY MODELS"],"prefix":"10.1017","volume":"18","author":[{"given":"Marine","family":"Carrasco","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2002,3,6]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602181023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T15:47:43Z","timestamp":1554565663000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602181023\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,2]]}},"alternative-id":["S0266466602181023"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602181023","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,2]]}}}