Functional limit theorems in Hölder space for residuals of nearly nonstationary AR(1) process

  1. Jurgita Markevičiūtė

Abstract

FUNCTIONAL LIMIT THEOREMS IN HÖLDER SPACE FOR RESIDUALS OF NEARLY NONSTATIONARY AR(1) PROCESS

We investigate the polygonal line process built on the residuals of the first order nearly nonstationary autoregressive process. We prove functional limit theorems in Hölder space in two cases: the autoregressive coefficient ϕn is defined as e=n, < 0 is a constant, and ϕn is defined as 1 − n=n, n ! 1, and n=n tends to zero as n ! 1. Also we discuss some applications of these functional limit theorems in epidemic change detection.

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Probability and Mathematical Statistics

37, z. 1, 2017

Strony od 163 do 183

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