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.
|Number of pages||6|
|Journal||Statistics & probability letters|
|Publication status||Published - 2008|