Abstract
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 seriesmodels, including the
GARCH(1, 1) process and its squares, the stochastic volatility models and solutions
to stochastic recurrence equations.
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 seriesmodels, including the
GARCH(1, 1) process and its squares, the stochastic volatility models and solutions
to stochastic recurrence equations.
| Original language | English |
|---|---|
| Journal | Probability Theory and Related Fields |
| Volume | 150 |
| Pages (from-to) | 337-372 |
| ISSN | 0178-8051 |
| DOIs | |
| Publication status | Published - Aug 2011 |