Least tail-trimmed absolute deviation estimation for autoregressions with infinite/finite variance

Abstract

We propose least tail-trimmed absolute deviation estimation for autoregressive processes with infinite/finite variance. We explore the large sample properties of the resulting estimator and establish its asymptotic normality. Moreover, we study convergence rates of the estimator under different moment settings and show that it attains a super-$\sqrt{n}$ convergence rate when the innovation variance is infinite. Simulation studies are carried out to examine the finite-sample performance of the proposed method and that of relevant statistical inferences. A real example is also presented.