Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

DOI10.1111/jtsa.12189zbMath1349.62407OpenAlexW2303476986MaRDI QIDQ2830682

Moritz Jirak

Publication date: 28 October 2016

Published in: Journal of Time Series Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/jtsa.12189

zbMATH Keywords

weak dependenceempirical distributionBerry-Esseenempirical quantile

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Cites Work

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• The Berry-Esséen type bound of sample quantiles for strong mixing sequence
• Berry-Esséen bound of sample quantiles for \(\varphi \)-mixing random variables
• Berry-Esseen theorems under weak dependence
• The functional central limit theorem for a family of GARCH observations with applications
• Augmented GARCH sequences: Dependence structure and asymptotics
• A Berry-Esseen theorem for sample quantiles under weak dependence
• Asymptotic results for the empirical process of stationary sequences
• Time series: theory and methods.
• On the Bahadur-Ghosh-Kiefer representation of sample quantiles
• Augmented GARCH\((p,q)\) process and its diffusion limit
• Generalized autoregressive conditional heteroscedasticity
• On the accuracy of the normal approximation for quantiles
• Modeling volatility persistence of speculative returns: a new approach
• Asymptotic spectral theory for nonlinear time series
• Mixing Markov shifts of kernel type are Bernoulli
• The isomorphism theorem for Bernoulli flows
• On the Bahadur representation of sample quantiles for dependent sequences
• Conditional Heteroskedasticity in Asset Returns: A New Approach
• Non-strong mixing autoregressive processes
• Iterated Random Functions
• Strong approximation of very weak Bernoulli processes
• Limit theorems for iterated random functions
• A Note on Quantiles in Large Samples
• Asymptotic Normality of Sample Quantiles for $m$-Dependent Processes

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