Componentwise different tail solutions for bivariate stochastic recurrence equations with application to ${\rm GARCH}(1,1)$ processes

2019 ◽  
Vol 155 (2) ◽  
pp. 227-254 ◽  
Author(s):  
Ewa Damek ◽  
Muneya Matsui ◽  
Witold Świątkowski
Keyword(s):  
Recurrence Equations ◽  
Stochastic Recurrence

scholarly journals Fractional Moments of Solutions to Stochastic Recurrence Equations

2013 ◽  
Vol 50 (4) ◽  
pp. 969-982 ◽  
Author(s):  
Thomas Mikosch ◽  
Gennady Samorodnitsky ◽  
Laleh Tafakori
Keyword(s):  
Stationary Solution ◽  
Numerical Study ◽  
Recurrence Equation ◽  
Erlang Distribution ◽  
Recurrence Equations ◽  
Stochastic Recurrence ◽  
Fractional Moments ◽  
Independent And Identically Distributed

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|X0|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.

scholarly journals Fractional Moments of Solutions to Stochastic Recurrence Equations

2013 ◽  
Vol 50 (04) ◽  
pp. 969-982 ◽  
Author(s):  
Thomas Mikosch ◽  
Gennady Samorodnitsky ◽  
Laleh Tafakori
Keyword(s):  
Stationary Solution ◽  
Numerical Study ◽  
Recurrence Equation ◽  
Erlang Distribution ◽  
Recurrence Equations ◽  
Stochastic Recurrence ◽  
Fractional Moments ◽  
Independent And Identically Distributed

In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equationXt=AtXt−1+Bt,t∈Z, where ((At,Bt))t∈Zis an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p,p∈R. Special attention is given to the case whenBthas an Erlang distribution. We provide various approximations to the moments E|X0|pand show their performance in a small numerical study.

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