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

Markevičiūtė J.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 1

163--183

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 eγ/n, γ < 0 is a constant, and ϕn is defined as 1 – γn/n, γn → ∞, and γn/n tends to zero as n → ∞. Also we discuss some applications of these functional limit theorems in epidemic change detection.