An autoregressive process with correlated random coefficients

A random coefficient autoregressive process is investigated in which the coefficients are correlated in the form of a moving average structure. First we give the stationary conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean and the usual least squares estimators of the process, such as convergence and asymptotic normality, supplied with the appropriate assumptions on the driving perturbations. Our objective is to get an overview of the influence of correlated coefficients in the moments of the process and the estimation step, through a simple model. In particular, the lack of consistency is shown. While convergence properties rely on the ergodicity, we use a martingale approach to reach asymptotic normalities.