Extended Glivenko-Cantelli theorem in ARCH\((p)\)-time series

DOI10.1016/J.SPL.2007.12.009zbMath1152.62363OpenAlexW2050460791MaRDI QIDQ945778

Fuxia Cheng

Publication date: 17 September 2008

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2007.12.009

Mathematics Subject Classification ID

Density estimation (62G07) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (4)

Extended Glivenko–Cantelli theorem and L₁ strong consistency of innovation density estimator for time-varying semiparametric ARCH model ⋮ The \(L_{1}\) strong consistency of ARCH innovation density estimator ⋮ Asymptotics of $L_\lambda$ -Norms of ARCH(p) Innovation Density Estimators ⋮ Asymptotics for L2-norm of ARCH innovation density estimator

Cites Work

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• Estimation in nonlinear time series models
• ARCH models and financial applications
• Residual analysis for \(\text{ARCH}(p)\)-time series.
• Fitting an error distribution in some heteroscedastic time series models
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Foundations of Modern Probability
• Some Results on the Complete and Almost Sure Convergence of Linear Combinations of Independent Random Variables and Martingale Differences

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