Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 59, No. 3, pp. 267-282 (2002)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



On the Extremal Behavior of Sub-Sampled Solutions of Stochastic Difference Equations

M.G. Scotto and K.F. Turkman

Center of Statistics, University of Lisbon -- PORTUGAL
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 $$ X_k=A_{k}X_{k-1}+B_k, k=1,2,..., $$ where $\{A_k,B_k\}$ are i.i.d. $\bkR^2$-valued random pairs. Let $Y_k=X_{Mk}$ be the sub-sampled 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
© 2002–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition