{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T05:37:04Z","timestamp":1791437824101,"version":"4.3.3"},"reference-count":41,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T00:00:00Z","timestamp":1612396800000},"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":[[2022,2]]},"abstract":"<jats:p>We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466620000584_inline1.png\"\/><jats:tex-math>\n$(X_t : t=1,2,\\ldots )$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466620000584_inline2.png\"\/><jats:tex-math>\n$X_t$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>\u2019s may load into the conditional covariance matrix of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466620000584_inline3.png\"\/><jats:tex-math>\n$X_t$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466620000584_inline4.png\"\/><jats:tex-math>\n$X_t$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.\n<\/jats:p>","DOI":"10.1017\/s0266466620000584","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T04:58:03Z","timestamp":1612501083000},"page":"1-34","source":"Crossref","is-referenced-by-count":2,"title":["CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH"],"prefix":"10.1017","volume":"38","author":[{"given":"Muneya","family":"Matsui","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rasmus S\u00f8ndergaard","family":"Pedersen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,2,4]]},"reference":[{"key":"S0266466620000584_r22","first-page":"503","article-title":"Spectral gap properties for linear random walks and Pareto\u2019s asymptotics for affine stochastic recursions","volume":"52","author":"Guivarc\u2019h","year":"2016","journal-title":"Annales de l\u2019Institut Henri Poincar\u00e9 (B) Probabilit\u00e9s et Statistiques"},{"key":"S0266466620000584_r19","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.06157"},{"key":"S0266466620000584_r7","doi-asserted-by":"publisher","DOI":"10.1137\/1110037"},{"key":"S0266466620000584_r16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600009063"},{"key":"S0266466620000584_r41","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478471"},{"key":"S0266466620000584_r36","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-017-0307-3"},{"key":"S0266466620000584_r1","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2011.571383"},{"key":"S0266466620000584_r8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2011.06.001"},{"key":"S0266466620000584_r13","unstructured":"Damek, E. & Matsui, M. 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