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The functional central limit theorem for a family of GARCH models

par Berkes, István;Hörmann, Siegfried ;Horvath, Lajos
Référence Statistics & probability letters, 78, 16, page (2725-2730)
Publication Publié, 2008

Article révisé par les pairs

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Résumé :

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.