Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to \(\mathrm{ARCH}(\infty)\) processes

DOI10.1016/j.camwa.2012.03.079zbMath1268.39014arXiv1202.5573OpenAlexW2091934491MaRDI QIDQ356154

John A. D. Appleby, John A. Daniels

Publication date: 25 July 2013

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5573

zbMATH Keywords

periodic solutiondifference equationadmissibilityVolterra equation\(\mathrm{ARCH}(\infty)\) processauto-covariance function

Mathematics Subject Classification ID

Volterra integral equations (45D05) Stability theory for difference equations (39A30)

Related Items (1)

Long run behaviour of the autocovariance function of ARCH(\(\infty\)) models

Cites Work

• Unnamed Item
• Long run behaviour of the autocovariance function of ARCH(\(\infty\)) models
• Change-point estimation in ARCH models
• ARCH-type bilinear models with double long memory.
• On exact convergence rates for solutions of linear systems of Volterra difference equations†
• Uniform asymptoic stability in linear volterra difference equations
• Perturbation Theory for Discrete Volterra Equations
• Perturbation of Volterra Difference Equations
• STATIONARITY AND MEMORY OF ARCH([infty infinity) MODELS]
• STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

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