Stable limits for sums of dependent infinite variance random variables
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Stable limits for sums of dependent infinite variance random variables. / Bartkiewicz, Katarszyna; Jakubowski, Adam ; Mikosch, Thomas Valentin; Wintenberger, Olivier .
In: Probability Theory and Related Fields, Vol. 150, No. 3-4, 2011, p. 337-372.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Stable limits for sums of dependent infinite variance random variables
AU - Bartkiewicz, Katarszyna
AU - Jakubowski, Adam
AU - Mikosch, Thomas Valentin
AU - Wintenberger, Olivier
PY - 2011
Y1 - 2011
N2 - The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.
AB - The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.
KW - Stationary sequence
KW - Stable limit distribution
KW - Weak convergence
KW - Mixing
KW - Weak dependence
KW - Characteristic function
KW - Regular variation
KW - GARCH
KW - Stochastic volatility model
KW - ARMA process
U2 - 10.1007/s00440-010-0276-9
DO - 10.1007/s00440-010-0276-9
M3 - Journal article
VL - 150
SP - 337
EP - 372
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
SN - 0178-8051
IS - 3-4
ER -
ID: 36006265