Naslov
J_1 convergence for partial sum processes with a reduced number of jumps

Autori
Krizmanić, Danijel

Izvornik
Probability and Mathematical Statistics-Poland (0208-4147) 35 (2015), 1; 107-128

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
functional limit theorem; partial sum process; regular variation; Skorohod J_1 topology; Levy process; weak dependence; mixing

Sažetak
Various functional limit theorems for partial sum processes of strictly stationary sequences of regularly varying random variables in the space of cadlag functions D[0, 1] with one of the Skorohod topologies have already been obtained. The mostly used Skorohod J_1 topology is inappropriate when clustering of large values of the partial sum processes occurs. When all extremes within each cluster of high-threshold excesses do not have the same sign, Skorohod M_1 topology also becomes inappropriate. In this paper we alter the definition of the partial sum process in order to shrink all extremes within each cluster to a single one, which allow us to obtain the functional J_1 convergence. We also show that this result can be applied to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and m- dependent sequences.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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