Nonlinear Models for U.K. Macroeconomic Time Series

This paper examines possible nonlinearities in growth rates of nine U.K. macroeconomic time series, namely gross domestic product, price, consumption, retail sales, personal disposable income, savings, investment, industrial production and unemployment, chosen as representative of series typically used to investigate business cycle fluctuations. By basing analysis on the class of smooth-transition autoregressive (STAR) models, it is assumed that the economy can be in one of two states with distinct dynamics or in transition between these states. Except for consumption, industrial production, and unemployment, I successfully estimate STAR models that pass a set of mis-specification tests. For the former three variables, the results indicate that two-threshold (three-regime) STAR models may be needed for a better description of their dynamics. The comparison of nonlinear models with their linear counterparts shows that although in most of the cases estimated nonlinear models yield lower residual variances and lower root-mean-square errors (RMSEs) in some cases, there is essentially no evidence of nonlinearity according to Diebold and Mariano's (1995) test of equal forecast accuracy. It is worthy of note that my modeling procedure with and without dummy variables introduced to account for abnormal observations suggests that these observations should not be overlooked within the context of STAR-type nonlinear modeling.