Generalized support vector machines (GSVMs) model for real-world time series forecasting

Support vector machines (SVMs) are one of the most popular and widely used approaches in modeling. Various kinds of SVM models have been developed in the literature of prediction and classification in order to cover different purposes. Fuzzy and crisp support vector machines are a well-known branch of modeling approaches frequently applied for certain and uncertain modeling, respectively. However, each model can only be efficiently used in its specified domain and cannot yield relevant and accurate results if the opposite situations have occurred. While the real-world systems and data sets often contain both certain and uncertain patterns that are complicatedly mixed and need to be simultaneously modeled. In this paper, a generalized support vector machine is proposed that can simultaneously benefit the unique advantages of certain and uncertain versions of the traditional support vector machines in their specialized categories. In the proposed model, the underlying data set is first categorized into two classes of certain and uncertain patterns. Then, certain patterns are modeled by a support vector machine, and uncertain patterns are modeled by a fuzzy support vector machine. After that, the function of the relationship, as well as the relative importance of each component, is estimated by another support vector machine. Finally, the forecasts of the proposed model are calculated. Empirical results of wind speed forecasting indicate that the proposed method not only can achieve more accurate results than support vector machines (SVMs) and fuzzy support vector machines but also can yield better forecasting performance than traditional fuzzy and nonfuzzy single models and traditional preprocessing-based hybrid models of SVMs.