On the Predictive Content of Nonlinear Transformations of Lagged Autoregression Residuals and Time Series Observations

Abstract Although many macroeconomic time series are assumed to follow nonlinear processes, nonlinear models often do not provide better predictions than their linear counterparts. Furthermore, nonlinear models easily become very complex and difficult to estimate. The aim of this study is to investigate whether simple nonlinear extensions of autoregressive processes are able to provide more accurate forecasting results than linear models. Therefore, simple autoregressive processes are extended by means of nonlinear transformations (quadratic, cubic, sine, exponential functions) of lagged time series observations and autoregression residuals. The proposed forecasting models are applied to a large set of macroeconomic and financial time series for 10 European countries. Findings suggest that these models, including nonlinear transformation of lagged autoregression residuals, are able to provide better forecasting results than simple linear models. Thus, it may be possible to improve the forecasting accuracy of linear models by including nonlinear components. This is especially true for time series that are positively tested for nonlinear characteristics and longer forecast horizons.