Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models

DOI10.1214/aos/1028144857zbMath0932.62064OpenAlexW2021890270MaRDI QIDQ1807086

Shiqing Ling

Publication date: 9 November 1999

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1028144857

zbMATH Keywords

weak convergenceBrownian motionsKiefer processsequential empirical processesnonstationary autoregressive model

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17) Foundations of stochastic processes (60G05)

Related Items (19)

Regression quantiles for unstable autoregressive models ⋮ Hill's estimator for the tail index of an ARMA model ⋮ The empirical process of autoregressive residuals ⋮ On the cusum of squares test for variance change in nonstationary and nonparametric time series models ⋮ Testing stochastic dominance with many conditioning variables ⋮ Covariance changes detection in multivariate time series ⋮ Testing hypotheses on the ``drift of parameters in ARMA and ARCH models ⋮ Weak convergence of the sequential empirical processes of residuals in TAR models ⋮ On residual empirical processes of GARCH-SM models: application to conditional symmetry tests ⋮ Change‐Point Tests for the Error Distribution in Non‐parametric Regression ⋮ Residual empirical processes for long and short memory time series ⋮ Fitting an error distribution in some heteroscedastic time series models ⋮ The Bickel--Rosenblatt test for diffusion processes ⋮ Diagnostic test for unstable autoregressive models ⋮ Sequential empirical process in autoregressive models with measurement errors ⋮ Testing the hypothesis on the ``drift of parameters in the moving average model ⋮ Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models ⋮ Factor and Idiosyncratic Empirical Processes ⋮ Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach

Cites Work

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• Weak convergence of the residual empirical process in explosive autoregression
• Limiting distributions of least squares estimates of unstable autoregressive processes
• Estimation of the distribution function of noise in stationary processes
• A weak convergence result useful in robust autoregression
• Weak convergence of the sequential empirical processes of residuals in ARMA models
• Estimation of the Distribution of Noise in an Autoregression Scheme
• ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications

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