Nonlinear Time Series: Models and Simulation

Abstract

Most financial time series exhibit nonlinear features which cannot be captured by the linear models seen in the previous two chapters. In this last chapter, we present the elements of a theory of nonlinear time series adapted to financial applications. We review a set of standard econometric models which were first introduced in the discrete time setting. They include the famous, ARCH, GARCH, … models, but we also discuss stochastic volatility models and we emphasize the differences between these concepts which are too often confused. However, because of the growing influence of the theoretical developments of continuous time finance in the everyday practice, we spend quite a significant part of the chapter analyzing the time series models derived from the discretization of continuous time stochastic differential equations.