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Contents of PMS, Vol. 37, Fasc. 1,
pages 163 - 183
 

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

Jurgita Markevičiūtė

Abstract: 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 ϕ
 n  is defined as eγ∕n  , γ < 0 is a constant, and ϕ
 n  is defined as 1- γ ∕n
    n , γ  → ∞
 n , and γ ∕n
 n tends to zero as n → ∞ . Also we discuss some applications of these functional limit theorems in epidemic change detection.

2010 AMS Mathematics Subject Classification: Primary: 60F17; Secondary: 62M10.

Keywords and phrases: Nearly nonstationary process, residuals, Hölderian functional limit theorems, epidemic change.

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