The \(L_{1}\) strong consistency of ARCH innovation density estimator

DOI10.1016/J.SPL.2011.01.001zbMath1209.62200OpenAlexW2025816493MaRDI QIDQ633047

Fuxia Cheng, Miin-Jye Wen

Publication date: 31 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.spl.2011.01.001

zbMATH Keywords

kernel density estimationstrong consistency\(L_{1}\)-normARCH-time series

Mathematics Subject Classification ID

Density estimation (62G07) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic properties of nonparametric inference (62G20)

Related Items (3)

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

Cites Work

• Extended Glivenko-Cantelli theorem in ARCH\((p)\)-time series
• The equivalence of weak, strong, and complete convergence in \(L_ 1\) for kernel density estimates
• ARCH models and financial applications
• \(L_{p}\)-estimators in ARCH models
• Residual analysis for \(\text{ARCH}(p)\)-time series.
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Asymptotic properties in ARCH(p)-time series

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