Dolomites Research Notes on Approximation

Kernel machines are widely used tools for extracting features from given data. In this context, there are many available techniques that are able to predict, within a certain tolerance, the evolution of time series, i.e. the dynamics of the considered quantities. However, the main drawback is that measurements are usually affected by noise/errors and might have gaps. For instance, gaps might be due to several problems of the physical instruments that produce measurements. In these cases the learning and prediction steps for capturing the trend of time series become very hard. To alleviate these difficulties, we construct a primary kernel-based approximant, which is indeed a model, with the double aim: to fill the gaps and to filter noisy data. The so-constructed smoothed samples are used as training sets for a kernel-based online model. We claim that the subsampled training phase makes the predicted results more stable. Applications to real data for environmental and financial observations support the validity of our results.