On the quasi-likelihood estimation for random coefficient autoregressions

We examine the Gaussian quasi-maximum likelihood estimator (QMLE) for random coefficient autoregressions. Consistency and asymptotic normality are established for general random coefficients and general correlation structure between these coefficients and the noise. In particular, the obtained results apply even if the stationary solution has infinite absolute mean or infinite variance. Next an application to the integer-valued times series modelling is given which provides a novel alternative for traditional INAR-like models for these series.