Stationary Arch Models: Dependence Structure and Central 
Limit Theorem

Giraitis, Liudas; Kokoszka, Piotr; Leipus, Remigijus

doi:10.1017/s0266466600161018

Cited by 213 publications

(165 citation statements)

References 17 publications

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“…According to Billingsley's result the FCLT follows if E(σ δ k − σ δ km ) 2 tends to zero sufficiently fast. We note that m-dependence was explored in Giraitis et al (2000) to obtain a central limit theorem for ARCH(∞) sequences.…”

Section: Resultsmentioning

confidence: 99%

The functional central limit theorem for a family of GARCH observations with applications

Berkes

Hörmann

Horváth

2008

Statistics & Probability Letters

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Please cite this article as: Berkes, I., Hörmann, S., Horváth, L., The functional central limit theorem for a family of GARCH observations with applications. Statistics and Probability Letters (2008Letters ( ), doi:10.1016Letters ( /j.spl.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M

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Section: Resultsmentioning

confidence: 99%

The functional central limit theorem for a family of GARCH observations with applications

Berkes

Hörmann

Horváth

2008

Statistics & Probability Letters

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“…If such a function has a mixing property fX t g is said to be F-mixing, and any -mixing fX t g is F-mixing covering linear and nonlinear ARMA-GARCH processes with su¢ ciently smooth probability densities (An and Huang 1996, Giraitis et al 2000, Carrasco and Chen 2002, Meitz and Saikkonen 2008.…”

Section: 3mentioning

confidence: 99%

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

Hill¹

2011

Econom. Theory

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New notions of tail and non-tail dependence are used to characterize separately extremal and non-extremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove Near Epoch Dependence (McLeish 1975, Gallant andWhite 1988) and L 0 -Approximability (Pötscher and Prucha 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence and tail trimmed sums of these data, allowing for Gaussian asymptotics for a new Tail-Trimmed Least Squares estimator for heavy tailed processes.

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“…The ARCH(1) representation is useful in considering properties of ARCH and GARCH models such as the existence of moments and long memory; see Giraitis, Kokoszka and Leipus (2000). The moment structure of GARCH models is considered in detail in 2007LINDNER.…”

Section: The Arch Modelmentioning

confidence: 99%

An Introduction to Univariate GARCH Models

Teräsvirta

2009

Handbook of Financial Time Series

102

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Stationary Arch Models: Dependence Structure and Central Limit Theorem

Cited by 213 publications

References 17 publications

The functional central limit theorem for a family of GARCH observations with applications

The functional central limit theorem for a family of GARCH observations with applications

Tail and Nontail Memory With Applications to Extreme Value and Robust Statistics

An Introduction to Univariate GARCH Models

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