Estimation in nonstationary random coefficient autoregressive models

Abstract

Abstract. We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model Xk = (ϕ + bk)Xk−1 + ek, where (ϕ, ω2, σ2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |ϕ + b0| ≥ 0 and show that σ2 cannot be estimated by the quasi‐maximum likelihood method. The asymptotic normality of the quasi‐maximum likelihood estimator for (ϕ, ω2) is proven so that the unit root problem does not exist in the RCA model.