Encyclopedia of Financial Models, 3 Volume Set

Nonlinearity and Nonlinear Econometric Models in Finance

RUEY S. TSAY, PhD

H.G.B. Alexander Professor of Econometrics and Statistics, University of Chicago Booth School of Business

Abstract:Many financial and economic data exhibit nonlinear characteristics. Prices of commodities such as crude oil often rise quickly but decline slowly. The monthly U.S. unemployment rate exhibits sharp increases followed by slow decreases. To model these characteristics in a satisfactory manner, one must employ nonlinear econometric models or use nonparametric statistical methods. For most applications, it suffices to employ simple nonlinear models. For example, the quarterly growth rate of the U.S. gross domestic product can be adequately described by the Markov switching or threshold autoregressive models. These models typically classify the state of the U.S. economy into two categories corresponding roughly to expansion and contraction.

In this entry, we study nonlinearity in financial data, discuss various nonlinear models available in the literature, and demonstrate application of nonlinear models in finance with real examples. The models discussed include bilinear models, threshold autoregressive models, smooth threshold autoregressive models, Markov switching models, and nonlinear additive autoregressive models. We also consider nonparametric methods and neural networks, and apply nonparametric methods to estimate interest models. To detect nonlinearity in financial data, we introduce ...