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This volume explains recent theoretical developments in the econometric modelling of relationships between different statistical series. The statistical techniques explored analyze relationships between different variables over time, such as the relationship between variables in a macroeconomy. Examples from Professor Terasvirta's empirical work are given. The authors are leading exponents of techniques of dynamic, multivariate analysis. They illustrate in this volume exploratory ways of using such techniques to provide models of nonlinear relationships between variables. This is an extension of previous work on linear relationships, and on univariate models. These developments should be of use to econometricians wishing to construct and use models of nonlinear, dynamic, multivariate relationships, such as investment function or a production function. Particular attention is paid to the case of a single dependent variable modelled by a few explanatory variables and the lagged dependent variable in nonlinear form. The book concentrates on stochastic series, since the existence of unexpected shocks strongly suggests that economic variables are stochastic. It also discusses the division of these nonlinear relationships into parametric and nonparametric models.