Functional central limit theorems for self-normalized partial sums of linear processes

DOI10.1007/s10986-011-9123-7zbMath1227.60029OpenAlexW2086081799MaRDI QIDQ647160

Charles Suquet, Alfredas Račkauskas

Publication date: 1 December 2011

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

Full work available at URL: https://doi.org/10.1007/s10986-011-9123-7

zbMATH Keywords

weak convergenceinvariance principledomain of attractionlinear processesself-normalization

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items

Self-normalized limit theorems for linear processes generated by \(\rho\)-mixing innovations ⋮ Modified unit root tests with nuisance parameter free asymptotic distributions ⋮ Further research on limit theorems for self-normalized sums ⋮ A general result on almost sure central limit theorem for self-normalized sums for mixing sequences ⋮ A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations ⋮ Complete moment convergence for moving average process based on m-WOD random variables ⋮ Complete moment convergence of moving average processes for m-WOD sequence ⋮ The Self-normalized Asymptotic Results for Linear Processes ⋮ Complete moment convergence for moving average process generated by \(\rho^{-}\)-mixing random variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On limit theorems for Banach-space-valued linear processes
• Limit theorems for self-normalized linear processes
• Recent advances in invariance principles for stationary sequences
• Pseudo-maximization and self-normalized processes
• Time series: theory and methods.
• The integrated periodogram for stable processes
• When is the Student \(t\)-statistic asymptotically standard normal?
• Donsker's theorem for self-normalized partial sums processes
• Invariance principles for adaptive self-normalized partial sums processes.
• Limit distributions of self-normalized sums
• A central limit theorem for self-normalized sums of a linear process
• Invariance principle for stochastic processes with short memory