A central limit theorem for random coefficient autoregressive models and ARCH/GARCH models

In this paper we study the so-called random coefficient autoregressive models and (generalized) autoregressive models with conditional heteroscedasticity. Both models can be represented as random systems with complete connections. Within this framework we are led (under certain conditions) to CL-regular Markov processes and we will give conditions under which (i) asymptotic stationarity, (ii) a law of large numbers and (iii) a central limit theorem can be shown for the corresponding models.