In the identification of nonlinear dynamical models it happens that not only the system dynamics have to be modeled but also the noise has a dynamic character. We show how to adapt Least Squares Support Vector Machines (LS-SVMs) to take advantage of a known or unknown noise model. We furthermore investigate a convex approximation based on over-parametrization to estimate a linear autoregressive noise model jointly with a model for the nonlinear system. Considering a noise model can improve generalization performance. We discuss several properties of the proposed scheme on synthetic data sets and finally demonstrate its applicability on real world data.