Estimation in nonstationary random coefficient autoregressive models

We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X_k = (ϕ + b_k)X_k - 1 + e_k, where (ϕ, omega-super-2, σ-super-2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |ϕ + b_0| >= 0 and show that σ-super-2 cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for (ϕ, omega-super-2) is proven so that the unit root problem does not exist in the RCA model. Copyright 2009 Blackwell Publishing Ltd