Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes
نویسندگان
چکیده
منابع مشابه
Spectral 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 کاملMultivariate 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 کاملParametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations
We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0, h, 2h, . . .). Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the observed MCARMA process. We use tools fro...
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 کاملExtremes of Regularly Varying Lévy Driven Mixed Moving Average Processes
In this paper we study the extremal behavior of stationary mixed moving average processes Y (t) = ∫ R+×R f(r, t − s) dΛ(r, s) for t ∈ R, where f is a deterministic function and Λ is an infinitely divisible independently scattered random measure, whose underlying driving Lévy process is regularly varying. We give sufficient conditions for the stationarity of Y and compute the tail behavior of ce...
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 Theoretical Probability
سال: 2011
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-011-0369-0