J1 convergence of partial sum processes with a reduced number of jumps

• Autorzy: Krizmanić D.
• Języki publikacji: EN

Abstrakty

EN

Various functional limit theorems for partial sum processes of strictly stationary sequences of regularly varying random variables in the space of càdlàg functions D[0, 1] with one of the Skorokhod topologies have already been obtained. The mostly used Skorokhod J₁ 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, Skorokhod M₁ 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 allows us to obtain the functional J₁ 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.

Słowa kluczowe

EN

functional limit theorem; partial sum process; regular variation; Skorokhod J1 topology; Lévy process; weak dependence; mixing

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 107--128
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Krizmanić D.

• Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).