engleski

Weak convergence of multivariate partial maxima processes

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 can not be replaced by the stronger (standard) M_1 topology. The theory is illustrated on three examples, including the multivariate squared GARCH process with constant conditional correlations.

functional limit theorem ; regular variation ; weak M_1 topology ; extremal process ; weak convergence ; multivariate GARCH

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