Estimation in nonstationary random coefficient autoregressive models

TL;DR

This paper studies parameter estimation in nonstationary random coefficient autoregressive models, showing limitations of quasi-maximum likelihood for some parameters and establishing asymptotic normality for others, thus addressing the unit root problem.

Contribution

It demonstrates that the innovation variance cannot be estimated via quasi-maximum likelihood in nonstationary RCA models and proves asymptotic normality for other parameters.

Findings

Innovation variance parameter cannot be estimated by QML.

Asymptotic normality of QML estimators for other parameters.

No unit root problem in the studied RCA models.

Abstract

We investigate the estimation of parameters in the random coefficient autoregressive model. We consider a nonstationary RCA process and show that the innovation variance parameter cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for the remaining model parameters is proven so the unit root problem does not exist in the random coefficient autoregressive model.