ABSTRACT

This chapter considers stationary discrete time models and focuses on parametric models which can be seen as generalizations of the AutoRegressive MovingAverage models. Several of the most important parametric non-linear models are described. The models are divided into two main classes of models depending on the purpose of the model: conditional mean and conditional variance. The chapter reviews some basic statistical theory. For the generalized method of moments (GMM) method no explicit assumption about the distribution of the observations is made, but the method can include such assumptions. In fact, it is possible to derive the maximum likelihood estimator as a very special case of the GMM estimator. A different class of models describing volatility changing over time is the class of stochastic volatility models. The chapter also discusses the applications of nonlinear models.