Multivariate Markov-switching ARMA processes with regularly varying noise
نویسندگان
چکیده
منابع مشابه
Multivariate Markov-switching ARMA processes with regularly varying noise
The tail behaviour of stationary R-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 particul...
متن کاملSpectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes
A spectral representation for regularly varying Lévy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the L2-case where the noise is a random orthogonal measure. This allows a spectral definition of multivariate regularly varying Lévy-driven continuous time autoregressive moving average (C...
متن کاملRegularly varying multivariate time series
Abstract: A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution of the rescaled series given that, at a fixed time instant, its distance to the origin exceeds a threshold tending to infinity. The limi...
متن کاملOn transformations of multivariate ARMA processes
Let Xt be an /-dimensional ARMA (p, q) process. Let g: U l -> W be a measurable function. Define a process Zt by Zt = g(Xt). Generally, Z.is not an ARMA process. However, we are interested in such functions g, for which Zt is also an AR process. It is important to know the orders of the process Zt. In the most cases we find only some bounds for them. From the practical point of view, our consid...
متن کاملThe cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sum...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2008
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2007.07.001