Specifying Nonlinear Econometric Models by Flexible Regression Models and Relative Forecast Performance

The paper considers the task of selecting a flexible nonlinear model which can be used as a baseline model. The baseline model may be used as a testing ground for more structural models which are congruent with economic theory. From the limited empirical evidence obtained here it is tentatively suggested to find a baseline nonlinear flexible form for a univariate time series by following the procedure: 1. Recursively, based on h extra periods at a time specify and estimate a linear form by use of model selection criteria like Cross Validation and/or BIC. 2. After a preliminary test for linearity, recursively, specify and estimate flexible regression models like the FNL suggested by Hamilton (1999) and the Projection Pursuit model suggested by Aldrin, Boelviken and Schweder (1993) for cases of moderate nonlinearities. Use the Cross Validation and the BIC criteria. 3. Based on the remaining part of the data set select the best nonlinear flexible form by use of forecast criteria measuring the absolute forecast performance and the directional forecast performance in h-steps ahead predictions, and compare the best flexible form to the linear specification by use of the Diebold Mariano tests, see Deibold and Mariano (1995) and the forecast encompassing tests suggested by Harvey, Lebourne, and Newhold (1998). The results indicate that the FNL method and the Projection Pursuit Model are the preferable models to apply and that the CV and BIC are the best selection criteria, while the forecast encompassing tests properly modified as suggested by Harvey et. al. (1998) possess better power properties than the Diebold- Mariano test