FUNCTIONAL LIMIT THEOREMS IN HÖLDER SPACE FOR RESIDUALSOF NEARLY NONSTATIONARYPROCESS
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 is defined as , is a constant, and
is defined as , , and tends to zero as . Also we
discuss some applications of these functional limit theorems in epidemic change detection.