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

István Berkes, Siegfried Hörmann and Lajos Horvath

Statistics & Probability Letters, 2008, vol. 78, issue 16, 2725-2730

Abstract: We consider polynomial variables which define an important subclass of Duan's augmented 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.

Date: 2008
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Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2725-2730