Fractional moments of solutions to stochastic recurrence equations

Mikosch, T, Samorodnitsky, G and Tafakori, L 2013, 'Fractional moments of solutions to stochastic recurrence equations', Journal of Applied Probability, vol. 50, no. 4, pp. 969-982.


Document type: Journal Article
Collection: Journal Articles

Title Fractional moments of solutions to stochastic recurrence equations
Author(s) Mikosch, T
Samorodnitsky, G
Tafakori, L
Year 2013
Journal name Journal of Applied Probability
Volume number 50
Issue number 4
Start page 969
End page 982
Total pages 14
Publisher Applied Probability Trust
Abstract In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt-1 + Bt, t ∈ ℤ, where ((At, Bt)) 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 Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.
Subject Probability Theory
Statistical Theory
Applied Statistics
Keyword(s) Moment
stochastic recurrence equation
GARCH
Erlang distribution
numerical approximation
DOI - identifier 10.1239/jap/1389370094
Copyright notice © Applied Probability Trust 2013
ISSN 0021-9002
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