Journal of Applied Probability

Fractional moments of solutions to stochastic recurrence equations

Thomas Mikosch, Gennady Samorodnitsky, and Laleh Tafakori

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Abstract

In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt-1 + Bt, tZ, where ((At, Bt))tZ is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p, pR. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.

Article information

Source
J. Appl. Probab., Volume 50, Number 4 (2013), 969-982.

Dates
First available in Project Euclid: 10 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1389370094

Digital Object Identifier
doi:10.1239/jap/1389370094

Mathematical Reviews number (MathSciNet)
MR3161368

Zentralblatt MATH identifier
1303.60042

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60K99: None of the above, but in this section

Keywords
Moment stochastic recurrence equation GARCH Erlang distribution numerical approximation

Citation

Mikosch, Thomas; Samorodnitsky, Gennady; Tafakori, Laleh. Fractional moments of solutions to stochastic recurrence equations. J. Appl. Probab. 50 (2013), no. 4, 969--982. doi:10.1239/jap/1389370094. https://projecteuclid.org/euclid.jap/1389370094


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