Asymptotic distributions related to mildly-explosive second order   autoregressive models
  In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the estimator has a Cauchy limit law which provides a bridge between moderate deviation asymptotics and the earlier results on the local to unity and explosive autoregressive models. In particular, the results can be applied to understand the near-integrated second order autoregressive processes. Simulation studies are also carried out to assess the performance of least squares estimation in finite samples. 
Hui Jiang, Mingming Yu, Guangyu Yang
math.PR math.ST stat.TH