Inference for Near-Integrated Time Series with Infinite Variance

Abstract

Abstract An autoregressive time series is said to be near-integrated (nearly nonstationary) if some of its characteristic roots are close to the unit circle. Statistical inference for the least squares estimators of near-integrated AR(1) models has been under rigorous study recently both in the statistics and econometric literatures. Although classical asymptotics are no longer available, through the study of weak convergence of stochastic processes, one can establish the asymptotic theories in terms of simple diffusion processes or Brownian motions. Such results rely heavily on the finiteness of the variance of the noise. When this finite variance condition fails, whereas many physical and economic phenomena are believed to be generated by an infinite variance noise sequence, the aforementioned asymptotics are not applicable. In this article, a unified theory concerning near-integrated autoregressive time series with infinite variance is developed. In particular, when the noise sequence {e t } belongs to...