Cross-Validation Error Criteria For Chaotic Time Series Prediction

Sadasivan Puthusserypady, Assistant Professor, Electrical & Computer Engineering, National University of Singapore

Prediction of chaotic time series can be implemented using machine learning methods, such as Radial Basis Function (RBF) networks. One common method of model selection is cross-validation, based on Mean Squared Error (MSE). The bias-variance dilemma dictates that there is an inevitable trade-off between bias and variance. Since invariants of chaotic systems are unchanged by linear transformations, it may be possible to accept more bias in the model. Hence, the use of error variance for model selection, instead of mean squared error, is examined. Clipping is introduced, as a simple way to stabilize iterated predictions. It is shown that using error variance for model selection, in combination with clipping, may result in better models.