Time series: theory and methods
Time series: theory and methods
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Multivariate linear recursions with Markov-dependent coefficients
Journal of Multivariate Analysis
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The tail behaviour of stationary R^d-valued Markov-switching ARMA (MS-ARMA) processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, it is established that these summability conditions are satisfied if the sum of the norms of the autoregressive parameters is less than one for all possible values of the parameter chain, which leads to feasible sufficient conditions. Our results complement in particular those of Saporta [Tail of the stationary solution of the stochastic equation Y"n"+"1=a"nY"n+b"n with Markovian coefficients, Stochastic Process. Appl. 115 (2005) 1954-1978.] where regularly varying tails of one-dimensional MS-AR(1) processes coming from consecutive large values of the parameter chain were studied.