This paper illustrates the Support Vector Method for the classification problem with two and more classes. In particular, the multi-class classification Support Vector Method of Weston and Watkins (1998) is correctly formulated as a quadratic optimization problem. Then, the method is applied to the problem of predicting business phases of the German economy. The generated support vectors are interpreted, in particular with respect to whether they are able to characterize business phase switches. Finally, the classification power of the Support Vector Method and of Linear Discriminant Analysis are compared. The results are two-fold. On the one hand, after the analysis of the results of this study it appears questionable that the Support Vector Method delivers an interpretable (dimension independent) data reduction by identifying the support vectors. Indeed, the support vectors did not appear to be sufficient to characterize the switches between the business phases. On the other hand, the classification power of the Support Vector Method was distinctly better than with Linear Discriminant Analysis. Note however that the Support Vector Method needs very much more computation time than Linear Discriminant Analysis.
support vector method multi-class classification linear discriminant analysis business cycle analysis