Abstract: We propose a unified quasi-likelihood procedure for the estimation of the unknown parameters of a first-order random coefficient autoregressive, RCA, model that works both for stationary and nonstationary processes. For this procedure, the weak consistency and the asymptotic normality are established under minimal assumptions on the noise sequences. In an empirical study, we highlight the practicality of the quasi-likelihood estimation for applications. As no initial knowledge about the probabilistic properties of the RCA process is required, our theoretical results immediately facilitate the statistical analysis for practitioners. They may, moreover, have an impact on the treatment of the prominent unit-root problems often encountered in econometrics.
Key words and phrases: Nonlinear optimization, nonlinear time series models, unit-roots.