The functional central limit theorem for a family of GARCH observations with applications
Siegfried Hörmann and
Statistics & Probability Letters, 2008, vol. 78, issue 16, 2725-2730
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.
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