PORTUGALIAE MATHEMATICA Vol. 59, No. 3, pp. 267282 (2002) 

On the Extremal Behavior of SubSampled Solutions of Stochastic Difference EquationsM.G. Scotto and K.F. TurkmanCenter of Statistics, University of Lisbon  PORTUGALand University of Aveiro, Department of Mathematics  PORTUGAL Center of Statistics, University of Lisbon  PORTUGAL Abstract: Let $\{X_k\}$ be a process satisfying the stochastic difference equation $$ X_k=A_{k}X_{k1}+B_k, k=1,2,..., $$ where $\{A_k,B_k\}$ are i.i.d. $\bkR^2$valued random pairs. Let $Y_k=X_{Mk}$ be the subsampled series corresponding to a fixed systematic sampling interval $M>1$. In this paper, we look at the extremal properties of $\{Y_k\}$. Motivation comes from the comparison of schemes for monitoring financial and environmental processes. The results are applied to the class of bilinear and ARCH processes. Keywords: Stochastic difference equation; systematic sampling; extreme values; extremal index; compound Poisson process; ARCH process; bilinear process. Classification (MSC2000): 60F05, 60G10, 60G70. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2002 Sociedade Portuguesa de Matemática
