Functional central limit theorems for sums of nearly nonstationary processes

DOI10.1007/s10986-012-9173-5zbMath1263.60027OpenAlexW1989707026MaRDI QIDQ1943760

Charles Suquet, Alfredas Račkauskas, Jurgita Markeviciute

Publication date: 21 March 2013

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-012-9173-5

zbMATH Keywords

functional central limit theoremBrownian motionpartial sumsmaximal inequalityHölder spaceautoregressive processpolygonal lineintegrated Ornstein-Uhlenbeck process

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Functional limit theorems; invariance principles (60F17)

Related Items (10)

Epidemic change tests for the mean of innovations of an AR(1) process ⋮ Testing mean changes by maximal ratio statistics ⋮ Testing epidemic change in nearly nonstationary process with statistics based on residuals ⋮ The Different Asymptotic Regimes of Nearly Unstable Autoregressive Processes ⋮ Hölderian weak invariance principle under a Hannan type condition ⋮ On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics ⋮ On the asymptotic of the maximal weighted increment of a random walk with regularly varying jumps: the boundary case ⋮ Hölderian weak invariance principle under the Maxwell and Woodroofe condition ⋮ Testing change in the variance with epidemic alternatives ⋮ CQR-based inference for the infinite-variance nearly nonstationary autoregressive models

Cites Work

• Necessary and sufficient condition for the functional central limit theorem in Hölder spaces
• Uniform Limit Theory for Stationary Autoregression
• Towards a unified asymptotic theory for autoregression
• Weak convergence of an autoregressive process used in modeling population growth
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