  This paper studies some temporal dependence properties and addresses the
issue of parametric estimation for a class of state-dependent autoregressive
models for nonlinear time series in which we assume a stochastic autoregressive
coefficient depending on the first lagged value of the process itself. We call
such a model state-dependent first-order autoregressive process, (SDAR). We
introduce some assumptions under which this class of models is strictly
stationary and uniformly ergodic and we establish consistency and asymptotic
normality of the quasi-maximum likelihood estimator of the parameters. In order
to capture the potentiality of the model, we present an empirical application
to nonlinear time series provided by the weekly realized volatility extracted
from returns of some European financial indices. The comparison of forecasting
accuracy is made considering an alternative approach provided by a two-regime
SETAR model
