Uniform asymptotic normality of weighted sums of short-memory linear processes. (March 2020)

• Record Type: Journal Article
• Authors: Norvaiša, Rimas; Račkauskas, Alfredas
• Is Part Of: Journal of applied probability. Volume 57:Number 1(2020)
• Page Start: 174
• Page End: 195
• Publication Date: 2020-03
• Subjects: Uniform limit theorem, -- weak invariance principle, -- p-variation, -- change points, -- regression, -- short memory linear process; 60F17, -- 62F05; 519.2
• DOI: 10.1017/jpr.2019.86
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Let $X_1, X_2, \dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let ${\mathcal{F}}$ be a bounded set of real-valued functions on [0, 1] with finite q -variation. It is proved that $\{n^{-1/2}\sum_{i=1}^nX_i\, f(i/n)\colon f\in{\mathcal{F}}\}$ converges in outer distribution in the Banach space of bounded functions on ${\mathcal{F}}$ as $n\to\infty$ . Several applications to a regression model and a multiple change point model are given.