Asymptotics for the random coefficient first-order autoregressive model with possibly heavy-tailed innovations

Abstract

Consider a random coefficient AR(1) model, Xt=(ρn+ϕn)Xt−1+ut, where {ρn,n≥1} is a sequence of real numbers, {ϕn,n≥1} is a sequence of random variables, and the innovations of the model form a sequence of i.i.d. random variables belonging to the domain of attraction of the normal law. By imposing some weaker conditions, the conditional least squares estimator of the autoregressive coefficient ρn is achieved, and shown to be asymptotically normal by allowing the second moment of the innovation to be possibly infinite.