Asymptotic inference for nearly nonstationary AR(1) processes with possibly infinite variance

In this article, the nearly nonstationary AR(1) processes, that is, Yt=βYt−1+εtYt=βYt−1+εt with β=1−γ/nβ=1−γ/n and γγ being a fixed constant, are studied under the condition that the disturbances of the processes are a sequence of i.i.d. random variables, which is in the domain of attraction of the normal law with zero means and possibly infinite variances. Compared with the result in Chan and Wei (1987), a more robust statistics about the least squares estimate of ββ is introduced.