In this talk, We studies the nonstationarity of the first-order double AR model. Based on this, it is shown that the quasi-maximum likelihood estimator of this model is consistent and asymptotically normal. We investigates also a quasi-maximum exponential likelihood estimator for a nonstationary GARCH (1,1) model. Asymptotic normality of this estimator is derived . Simulation studies are carried out to assess the performance of the quasi-maximum likelihood estimator/quasi-maximum exponential likelihood estimator in finite samples.