Abstract
In this paper, we consider parameter estimation problems in the first order nearly nonstationary autoregression AR(1) model, which is described by formula (2.1). By allowing the most general class of innovations, we extend the result of Chan and Wei [1]. Moreover, we discuss a sequential procedure for estimating the parameter, extending the result of Lai and Siegmund [2] and Greenwood and Shiryaev [3] to the nearly nonstationary model. The results are essentially based on the preliminary Theorems 1 and 2, stating the weak convergence, as the sample size grows, of an observed nearly nonstationary AR(1) process to a corresponding AR(1) process in continuous time.
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