Weak convergence of multivariate partial maxima processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:155

Article

Krizmanic, Danijel¹ 

[1] Univ Rijeka, Dept Math, Radmile Matejcic 2, Rijeka 51000, Croatia

关键词: Functional limit theorem;    Regular variation;    Weak M-1 topology;    Extremal process;    Weak convergence;    Multivariate GARCH;   

DOI  :  10.1016/j.jmva.2016.11.012

来源: Elsevier

【 摘 要 】

For a strictly stationary sequence of R-+(d)-valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an extremal process and the convergence takes place in the space of R-+(d)-valued cadlag functions on [0, 1], with the Skorohod weak M-1 topology. We also show that this topology in general cannot be replaced by the stronger (standard) M-1 topology. The theory is illustrated on three examples, including the multi-variate squared GARCH process with constant conditional correlations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free