On Asymptotic Theory for ARCH (∞) Models

Christian M. Hafner; Arie Preminger

doi:10.1111/jtsa.12239

On Asymptotic Theory for ARCH (∞) Models

Christian M. Hafner
, Arie Preminger

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Autoregressive conditional heteroskedasticity (ARCH)(∞) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH(∞) class of models and develops the theory for consistency and asymptotic normality of the quasi-maximum likelihood estimator.

Original language	English
Pages (from-to)	865-879
Number of pages	15
Journal	Journal of Time Series Analysis
Volume	38
Issue number	6
DOIs	https://doi.org/10.1111/jtsa.12239
State	Published - 1 Nov 2017
Externally published	Yes

Keywords

Volatility
fractional integration
long memory
quasi-maximum likelihood

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1111/jtsa.12239

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abstract = "Autoregressive conditional heteroskedasticity (ARCH)(∞) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH(∞) class of models and develops the theory for consistency and asymptotic normality of the quasi-maximum likelihood estimator.",

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AU - Preminger, Arie

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AB - Autoregressive conditional heteroskedasticity (ARCH)(∞) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH(∞) class of models and develops the theory for consistency and asymptotic normality of the quasi-maximum likelihood estimator.

KW - Volatility

KW - fractional integration

KW - long memory

KW - quasi-maximum likelihood

UR - https://www.scopus.com/pages/publications/85018728102

U2 - 10.1111/jtsa.12239

DO - 10.1111/jtsa.12239

M3 - Article

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JF - Journal of Time Series Analysis

IS - 6

ER -

On Asymptotic Theory for ARCH (∞) Models

Abstract

Keywords

ASJC Scopus subject areas

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