Nonlinear Time Series With Long Memory: A Model for Stochastic Volatility

We introduce a nonlinear model of stochastic volatility within the class of product type models. It allows different degrees of dependence for the raw series and for the squared series, for instance implying weak dependence in the former and long memory in the latter. We discuss its main statistical properties with respect to the common set of stylized facts characterizing financial assets returns time series dynamics, and apply it to several series of asset returns.