Geodesic
Gaussian approximation for residuals of stationary autoregressive process in H\"{o}lder norm
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 19-33

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The paper treats the hölderian approximation for partial sums process of stationary autoregressive residuals (AR(p), $p \geq 1$). 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 $\alpha\frac{1}{2}$. A statistical application of this convergence to detect epidemic change and simulation results are also presented.
Keywords: Autoregressive model, Brownian motion, Hölder space, invariance principle, partial sums process, residuals. 
@article{THSP_2017_22_2_a2,
     author = {K. Ime\c{c}aoudene and D. Hamadouche},
     title = {Gaussian approximation for residuals of stationary autoregressive process in {H\"{o}lder} norm},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {19--33},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a2/}
}
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K. Imeçaoudene; D. Hamadouche. Gaussian approximation for residuals of stationary autoregressive process in H\"{o}lder norm. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 19-33. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a2/