The functional central limit theorem for a family of GARCH models

István I. Berkes; Siegfried Hörmann; Lajos Horvath

The functional central limit theorem for a family of GARCH models

István I. Berkes, Siegfried Hörmann, Lajos Horvath

Institute of Statistics (5060)

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

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 language	Undefined/Unknown
Pages (from-to)	2725-2730
Number of pages	6
Journal	Statistics & Probability Letters
Volume	78
Issue number	16
Publication status	Published - 2008

Access to Document

http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/48613

Cite this

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title = "The functional central limit theorem for a family of GARCH models",

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.",

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AU - Hörmann, Siegfried

AU - Horvath, Lajos

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PY - 2008

Y1 - 2008

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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VL - 78

SP - 2725

EP - 2730

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

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