State-Dependent Autoregressive Model for Nonlinear Time Series: Stationarity, Ergodicity and Estimation Methods

Abstract

This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models 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 processes, SDAR(1). 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.