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In this paper, we consider the normalized least squares estimator of theparameter in a mildly-explosive first-order autoregressive model with dependenterrors which are modeled as a mildly-explosive AR(1) process. We prove that theestimator has a Cauchy limit law which provides a bridge between moderatedeviation asymptotics and the earlier results on the local to unity andexplosive autoregressive models. In particular, the results can be applied tounderstand the near-integrated second order autoregressive processes.Simulation studies are also carried out to assess the performance of leastsquares estimation in finite samples.

Asymptotic distributions related to mildly-explosive second order autoregressive models