Taqqu, Murad S.Bai, Shuyang2020-01-212020-01-212013-10-22Murad S Taqqu, Shuyang Bai. 2013. "Multivariate limit theorems in the context of long-range dependence." Journal of Time Series Analysis, Volume 34, Issue 6, pp. 717 - 743. https://doi.org/10.1111/jtsa.120460143-9782https://hdl.handle.net/2144/39127We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multivariate Gaussian process involving dependent Brownian motion marginals, or (b) a multivariate process involving dependent Hermite processes as marginals, or (c) a combination. We treat cases (a), (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary.p. 717 - 743en-USScience & technologyPhysical sciencesMathematics, interdisciplinary applicationsStatistics & probabilityMathematicsLong-range dependenceGaussian processCentral limit theoremsNon-central limit theoremsAsymptotic independenceMultiple Wiener-Ito integralsStationary Gaussian-processesNonlinear functionalsIndependenceIntegralsFieldsStatisticsEconometricsArticle10.1111/jtsa.120460000-0002-1145-9082 (Taqqu, Murad S)34285