Multivariate Markov-switching ARMA processes with regularly varying noise

The tail behaviour of stationary Rd-valued Markov-Switching 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, the feasible stationarity condition given in Stelzer (2006) is extended to a criterion for regular variation. Our results complement in particular those of Saporta (2005) where regularly varying tails of one-dimensional MS-AR(1) processes coming from consecutive large parameters were studied.     «

The tail behaviour of stationary Rd-valued Markov-Switching 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, the feasible stationarity condition given in Stelzer (2006) is extended to a criterion for regular variation. Our results complement in particular those of Saporta (2005) where regularly varying tails of one-dimensional MS-AR(1) processes comin...     »