On the quasi-likelihood estimation for random coefficient autoregressions

Abstract

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.

Keywords:

• quasi-likelihood estimation
• random coefficient autoregressions
• integer-valued time series

2000 Mathematics Subject Classification :

• Primary: 62M10
• secondary: 62M20

Notes

The authors would like to thank Pierre Boivin from the Health and Social Services (Direction of public health, Department of infectious diseases) in Roberval (Québéc) Canada and Alain Latour from University of Grenoble (France), who kindly provided the data set.