Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 37, Number 4 (2005), 993-1014.
Extremes of regularly varying Lévy-driven mixed moving average processes
In this paper, we study the extremal behavior of stationary mixed moving average processes of the form Y(t)=∫ℝ+×ℝf(r,t-s) dΛ(r,s), 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 certain functionals of Y. The extremal behavior is modeled by marked point processes on a discrete-time skeleton chosen properly by the jump times of the underlying driving Lévy process and the extremes of the kernel function. The sequences of marked point processes converge weakly to a cluster Poisson random measure and reflect extremes of Y at a high level. We also show convergence of the partial maxima to the Fréchet distribution. Our models and results cover short- and long-range dependence regimes.
Adv. in Appl. Probab. Volume 37, Number 4 (2005), 993-1014.
First available in Project Euclid: 14 December 2005
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Continuous-time moving average process extreme-value theory independently scattered random measure long-range dependence marked point process point process regular variation shot noise process supOU process
Fasen, Vicky. Extremes of regularly varying Lévy-driven mixed moving average processes. Adv. in Appl. Probab. 37 (2005), no. 4, 993--1014. doi:10.1239/aap/1134587750. http://projecteuclid.org/euclid.aap/1134587750.