Fractional Moments of Solutions to Stochastic Recurrence Equations

In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation X t = A t X t−1 + B t , t ∈ Z, where ((A t , B t )) t∈Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X 0| p ,...

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Bibliographic Details
Published in:Journal of applied probability 2013-12, Vol.50 (4), p.969-982
Main Authors: Mikosch, Thomas, Samorodnitsky, Gennady, Tafakori, Laleh
Format: Article
Language:English
Subjects:
60G70
60K99
Approximation
Distributivity
Erlang distribution
GARCH
Grants
Integers
Mathematical moments
Mathematical problems
Moment
Numerical analysis
numerical approximation
Probability distribution
Random variables
Research grants
Research universities
Stochastic models
stochastic recurrence equation
Studies
Time series analysis
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Summary:In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation X t = A t X t−1 + B t , t ∈ Z, where ((A t , B t )) t∈Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X 0| p , p ∈ R. Special attention is given to the case when B t has an Erlang distribution. We provide various approximations to the moments E|X 0| p and show their performance in a small numerical study.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1389370094