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

Sabrina Mulinacci

In this talk we consider a specific class of state-dependent autoregressive models in which we assume a stochastic autoregressive coefficient that depends on the first lagged value of the process itself. We call such a model state-dependent first-order autoregressive process, SDAR(1). From a theoretical point of view, 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. From a more practical perspective, we consider some particular examples of the model more suitable for applications (joint work with Fabio Gobbi).