The scope of this paper is twofold. We first describe the tail behavior for general AR-GARCH processes and hence extend the results of Basrak, Davis, and Mikosch (2002b) to another empirical relevant model class. Second, and primarily, we study properties for the OLS estimator in general AR-GARCH model. Specifically it is shown that the OLS estimator of the autoregressive parameter in the AR-GARCH model has a non-standard limiting distribution with a non-standard rate of convergence when the innovations have non-finite fourth order moment.