Generalized Fock spaces (GFS) were proposed some time ago as a general framework for non-linear system identification and signal analysis. Corresponding to a particular class of reproducing kernel Hubert spaces (RKHS) they provide a natural framework for the estimation of continuous- and discrete-time Volterra filters (VF). Whilst both finite and infinite degree VF are treated in a single framework using GFS an open question is the practical estimation of infinite degree VF. In this paper this problem is resolved and it is shown how VF of arbitrary degree (including infinite) can be computed with finite resources. The solutions are global best approximations to the entire VF based on the available data. Use is made of recent advances in the machine learning community, such as the support vector machine, which make extensive use of RKHS ideas. This paper also highlights the importance of this work to the system identification community. A number of particular contributions are made including a derivation of a particular GFS for VF which permits a simply computable reproducing kernel, derivations of the associated mappings between Volterra parameter space and RKHS parameter space which permit the extraction of the Volterra parameters from the RKHS approximation and solve a set of ``free'' parameters, extending the GFS framework to include regularization and a detailed simulation-based comparison of the estimation of VF.