Modelling Nonlinear Economic Time Series

Abstract

This book contains a up-to-date overview of nonlinear time series models and their application to modelling economic relationships. It considers nonlinear models in stationary and nonstationary frameworks, and both parametric and nonparametric models are discussed. The book contains examples of nonlinear models in economic theory and presents the most common nonlinear time series models. Importantly, it shows these models can be applied in practice. For this purpose, the building of various nonlinear models with its three stages of model building: specification, estimation, and evaluation, is discussed in detail and is illustrated by several examples involving both economic and non-economic data. Since estimation of nonlinear time series models is carried out using numerical algorithms, the book contains a chapter on estimating parametric nonlinear models and another on estimating nonparametric ones. Forecasting is a major reason for building time series models, linear or nonlinear. The book contains a discussion on forecasting with nonlinear models, both parametric and nonparametric, and considers numerical techniques necessary for computing multi-period forecasts from them. The main focus of the book is on models of the conditional mean, but models of the conditional variance, mainly those of autoregressive conditional heteroskedasticity, receive attention as well. A separate chapter is devoted to state space models.

Economic Policy Uncertainty and Unemployment in the United States: A Nonlinear Approach

“…A technical note is in order. Teräsvirta, Tjøstheim, and Granger (2010) point out that is not a scale-free parameter. To make it scale free, we follow their suggestion (p. 381 of their book) and standardize the transition indicator so that z t features a mean equal to zero and a standard deviation equal to one.…”

“…1 Given z t , we jointly estimate the parameters f R ; E ; ; ; cg of model (1)- (3) with conditional maximum likelihood as suggested by Teräsvirta, Tjøstheim, and Granger (2010). We model the vector of data X t = [EP U D t ; IP t ; u t ; t ; R t ] 0 .…”

Understanding the Link Between Aggregated Industrial Production and the Carbon Price

“…In the second step, once the presence of the threshold(s) has been confirmed, we aim at identifying whether a model with one or two thresholds is preferable (see Teräsvirta et al (2011) for more details).…”

Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

“…Thus, various regime switching, threshold autoregression and smooth transition models have been used extensively to capture and gauge these effects (see, e.g., [16][17][18][19][20][21] for overviews of such models). In the models with moving order statistics and moving sample quantiles (MQ) as their generalization, the order statistics-linked effects directly reveal the importance of the different sizes of realizations observed within a sample.…”