Uniform AR(1) processes and maxima on partial samples

Abstract

Let (Xn)n1 be the uniform AR(1) process with parameter r 2, and (cn)n1 a 0-1 sequence such that the limit exists. Let be the maximum of those Xks for which k n and ck = 1, and Mn = max {X1,., Xn}. We prove that the limit distribution of the random vector as n → ∞ is not uniquely determined by the limit value p. A simulation study and analysis of a simulated data set are presented. The cases when the partial maximum is determined by certain point processes are included in the simulation study.