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The availability of complex data structures motivates a renewal interest on developing statistical tools and methods to discover latent structures. Undoubtedly, most successfully techniques, such as classification trees and  support vector machines (SVM), have been originated within the machine learning literature, and lack of solid inferential procedures. Building on the existing literature, we extend SVM methods for classification and regression to model conditional quantiles at a given confidence level $\tau\in\left(0,1\right)$.  A new data augmentation schemes that facilitates Gibbs updating schemes as well as EM--type algorithms is introduced. As a further contribution we extend the static SVM quantile regression to a dynamic framework where the parameters are stochastic processes having their own dynamic. Several applications on real dataset illustrate the model and inference procedures.