UNIVERSITY
OF WROC£AW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 42.1 41.2 41.1 40.2 40.1
39.2 39.1 38.2 38.1 37.2 37.1 36.2
36.1 35.2 35.1 34.2 34.1 33.2 33.1
32.2 32.1 31.2 31.1 30.2 30.1 29.2
29.1 28.2 28.1 27.2 27.1 26.2 26.1
25.2 25.1 24.2 24.1 23.2 23.1 22.2
22.1 21.2 21.1 20.2 20.1 19.2 19.1
18.2 18.1 17.2 17.1 16.2 16.1 15
14.2 14.1 13.2 13.1 12.2 12.1 11.2
11.1 10.2 10.1 9.2 9.1 8 7.2
7.1 6.2 6.1 5.2 5.1 4.2 4.1
3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 35, Fasc. 1,
pages 107 - 128
 

J1  CONVERGENCE OF PARTIAL SUM PROCESSES WITH A REDUCED NUMBER OF JUMPS

Danijel Krizmanić

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

2000 AMS Mathematics Subject Classification: Primary: 60F17; Secondary: 60G52, 60G55.

Keywords and phrases: Functional limit theorem, partial sum process, regular variation, Skorokhod J1  topology, Lé vy process, weak dependence, mixing.

Download:    Abstract    Full text   Abstract + References