Sequential input selection algorithm for long-term prediction of time series

In time series prediction, making accurate predictions is often the primary goal. At the same time, interpretability of the models would be desirable. For the latter goal, we have devised a sequential input selection algorithm (SISAL) to choose a parsimonious, or sparse, set of input variables. Our proposed algorithm is a sequential backward selection type algorithm based on a cross-validation resampling procedure. Our strategy is to use a filter approach in the prediction: first we select a sparse set of inputs using linear models and then the selected inputs are used in the nonlinear prediction conducted with multilayer-perceptron networks. Furthermore, we perform a sensitivity analysis by quantifying the importance of the individual input variables in the nonlinear models using a method based on partial derivatives. Experiments are done with the Santa Fe laser data set that exhibits very nonlinear behavior and a data set in a problem of electricity load prediction. The results in the prediction problems of varying difficulty highlight the range of applicability of our proposed algorithm. In summary, our SISAL yields accurate and parsimonious prediction models giving insight to the original problem.