Out-of-Sample Forecasts and Nonlinear Model Selection with an Example of the Term Structure of Interest Rates

It is well known that goodness-of-fit measures lead to overfitting. We compare the small-sample properties of linear and several nonlinear models using a Monte Carlo study. A large number of linear series are generated and conventional methods of fitting nonlinear models are applied to each. The best linear and nonlinear models are compared using in-sample and out-of-sample criteria. Out-of-sample forecasts are shown to be superior for selecting the proper specification. The experiment is repeated using a nonlinear model and the in-sample fit and forecasts of the various models are compared. An example is provided using the term structure of interest rates.