On the predictive content of nonlinear transformations of lagged autoregression residuals and time series observations

This study focuses on the question whether nonlinear transformation of lagged time series values and residuals are able to systematically improve the average forecasting performance of simple Autoregressive models. Furthermore it investigates the potential superior forecasting results of a nonlinear Threshold model. For this reason, a large-scale comparison over almost 400 time series which span from 1996:3 up to 2008:12 (production indices, price indices, unemployment rates, exchange rates, money supply) from 10 European countries is made. The average forecasting performance is appraised by means of Mean Group statistics and simple t-tests. Autoregressive models are extended by transformed first lags of residuals and time series values. Whereas additional transformation of lagged time series values are able to reduce the ex-ante forecast uncertainty and provide a better directional accuracy, transformations of lagged residuals also lead to smaller forecast errors. Furthermore, the nonlinear Threshold model is able to capture certain type of economic behavior in the data and provides superior forecasting results than a simple Autoregressive model. These findings are widely independent of considered economic variables.