Index Tracking by Using Sparse Support Vector Regression

In this paper a sparse support vector regression (SVR) model and its solution method are considered for the index tracking problem. The sparse SVR model is structured by adding a cardinality constraint in a epsilon-SVR model and the piecewise linear functions are used to simplify the model. In addition, for simplifying the parameter selection of the model a sparse variation of the v-SVR model is considered too. The two models are solved by utilizing the penalty proximal alternating linearized minimization (PALM) method and the structures of the two models satisfy the convergence conditions of the penalty PALM method. The numerical results with practical data sets demonstrate that for the fewer sample data the sparse SVR models have better generalization ability and stability especially for the large-scale problems.