Gaussian approximation for residuals of stationary autoregressive process in Hölder norm

K. Imeçaoudene, D. Hamadouche
Theory of Stochastic Processes
Vol.22 (38), no.2, 2017, pp.19-33
The paper treats the hölderian approximation for partial sums process of stationary autoregressive residuals (AR(p), p ≥ 1). We consider the polygonal smoothed process of these partial sums and we prove the Hölder convergence of this sequence of processes to the Brownian motion for any order α < 1/2. A statistical application of this convergence to detect epidemic change and simulation results are also presented.