CQR-based inference for the infinite-variance nearly nonstationary autoregressive models

We consider the nearly nonstationary autoregressive model y(t) = q(n)y(t-1)+u(t), where q(n) = 1-c/n, c is a fixed constant, and {u(t), t >= 1} is a sequence of innovations belonging to the domain of attraction of a stable distribution with index 0 < alpha < 2. We construct a composite quantile regression estimator for the autoregressive coefficient and establish the asymptotic distribution of this estimator under some mild conditions.