The functional central limit theorem for a family of GARCH models

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Abstract

We consider polynomial GARCH(p,q) variables which define an important subclass of Duan's augmented GARCH(p,q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey--Fuller statistics under optimal conditions.
Original languageUndefined/Unknown
Pages (from-to)2725-2730
Number of pages6
JournalStatistics & probability letters
Volume78
Issue number16
Publication statusPublished - 2008

Cite this

The functional central limit theorem for a family of GARCH models. / Berkes, István I.; Hörmann, Siegfried; Horvath, Lajos.

In: Statistics & probability letters, Vol. 78, No. 16, 2008, p. 2725-2730.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Hörmann, Siegfried

AU - Horvath, Lajos

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N2 - We consider polynomial GARCH(p,q) variables which define an important subclass of Duan's augmented GARCH(p,q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey--Fuller statistics under optimal conditions.

AB - We consider polynomial GARCH(p,q) variables which define an important subclass of Duan's augmented GARCH(p,q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey--Fuller statistics under optimal conditions.

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JF - Statistics & probability letters

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