The growing complexity of cyber-physical systems, together with increasingly available parallelism provided by multi-core chips, fosters the parallelization of simulation. Simulation speed-ups are expected from co-simulation and parallelization based on model splitting into weakly coupled submodels, such as in the framework of a functional mockup interface. However, slackened synchronization between submodels and their associated solvers running in parallel introduces integration errors, which must be kept inside acceptable bounds. CHOPtrey denotes a forecasting framework enhancing the performance of complex system co-simulation, with a trivalent articulation. First, we consider the framework of a computationally hasty online prediction system. It allows to improve the tradeoff between integration speed-ups, needing large communication steps, and simulation precision, needing frequent updates for model inputs. Second, smoothed adaptive forward prediction improves co-simulation accuracy. It is obtained by past-weighted extrapolation based on causal hopping oblivious polynomials. Third, signal behavior is segmented to handle the discontinuities of the exchanged signals: the segmentation is performed in a contextual and hierarchical ontology of patterns. Implementation strategies and simulation results demonstrate the framework ability to adaptively relax data communication constraints beyond synchronization points which sensibly accelerate the simulation. The CHOPtrey framework extends the range of applications of standard Waring-Lagrange polynomial extrapolation, often deemed unstable. The embedding of predictions in lag-dependent smoothing and discontinuity handling demonstrates its practical efficiency.