Estimation in nonstationary random coefficient autoregressive models

We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X(k) = (phi + b(k))X(k-1) + e(k), where (phi, omega(2), Sigma(2)) is the parameter of the process. We consider a nonstationary RCA process satisfying E log vertical bar phi + b(0)vertical bar >= 0 and show that Sigma(2) cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for (phi, omega(2)) is proven so that the unit root problem does not exist in the RCA model.