Weak convergence of multivariate partial maxima processes

2016/07/13 by Danijel Krizmanić, Krizmanić, Danijel
Economics, Econometrics and Finance · Decision Sciences · #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1607.03788

Abstract

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 càdlàg functions on [0,1], with the Skorohod weak M₁ topology. We also show that this topology in general can not be replaced by the stronger (standard) M₁ topology. The theory is illustrated on three examples, including the multivariate squared GARCH process with constant conditional correlations.

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