Notes on Nonlinear Dynamics

Abstract

We present a selective survey of modern nonlinear modeling techniques relevant to the field of applied financial econometrics. We first established the usefulness of nonlinear modeling of financial time series and its relevance for forecasting by means of Sims’s (1984) definition. Then, we describe specific univariate and multivariate nonlinear models that can be classified either as stochastic or as deterministically chaotic. We also provide several novel numerical applications of these models along with their estimation techniques and tests. We conclude this literature review by presenting an application which compares the UHF‐GARCH model with the parsimonious model‐free realized volatility approach. Additionally, we present an extension to the multivariate case, referred as the realized covariance. This model‐free measure of dependence might be useful in order to evaluate the volatility feedback, which is an alternative explanation to the leverage effect theory.