Motivation: Reverse engineering of gene regulatory networks remains a central challenge in computational systems biology, despite recent advances facilitated by benchmark in-silico challenges that have aided in calibrating their performance. A number of approaches using either perturbation (knock-out) or wild-type time series data have appeared in the literature addressing this problem, with the latter employing linear temporal models. Nonlinear dynamical models are particularly appropriate for this inference task given the generation mechanism of the time series data. In this study, we introduce a novel nonlinear autoregressive model based on operator-valued kernels that simultaneously learns the model parameters, as well as the network structure. Model and Methods: A flexible boosting algorithm (OKVAR-Boost) that shares features from L2-boosting and randomization-based algorithms is developed to perform the tasks of parameter learning and network inference for the proposed model. Specifically, at each boosting iteration, a regularized operator-valued kernel based vector autoregressive model (OKVAR) is trained on a random subnetwork. The final model consists of an ensemble of such models. The empirical estimation of the ensemble model's Jacobian matrix provides an estimation of the network structure. Results:This study makes a number of key contributions to the challenging problem of network inference based solely on time course data. It introduces a powerful network inference framework based on nonlinear autoregressive modeling and Jacobian estimation. The proposed framework is rich and flexible, employing penalized regression models that coupled with randomized search algorithms and features of L2-boosting prove particularly effective as the extensive simulation results attest. The models employed require tuning of a number of parameters and we introduce a novel and generally applicable strategy that combines bootstrapping with stability selection to achieve this goal. The performance of the proposed algorithm is first evaluated on a number of benchmark data sets from the DREAM3 challenge and then, on real datasets related to the IRMA and T-cell networks. The high quality results obtained strongly indicate that it outperforms existing approaches.