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Statistic modeling and data-driven learning are the two vital fields thatattract many attentions. Statistic models intend to capture and interpret therelationships among variables, while data-based learning attempt to extractinformation directly from the data without pre-processing through complexmodels. Given the extensive studies in both fields, a subtle issue is how toproperly integrate data based methods with existing knowledge or models. Inthis paper, based on the time series data, we propose two different directionsto integrate the two, a decomposition-based method and a method exploiting thestatistic extraction of data features. The first one decomposes the data intolinear stable, nonlinear stable and unstable parts, where suitable statisticalmodels are used for the linear stable and nonlinear stable parts while theappropriate machine learning tools are used for the unstable parts. The secondone applies statistic models to extract statistics features of data and feedthem as additional inputs into the machine learning platform for training. Themost critical and challenging thing is how to determine and extract thevaluable information from mathematical or statistical models to boost theperformance of machine learning algorithms. We evaluate the proposal using timeseries data with varying degrees of stability. Performance results show thatboth methods can outperform existing schemes that use models and learningseparately, and the improvements can be over 60%. Both our proposed methods arepromising in bridging the gap between model-based and data-driven schemes andintegrating the two to provide an overall higher learning performance.

Two ways towards combining Sequential Neural Network and Statistical Methods to Improve the Prediction of Time Series