The dynamics of the suction manifold of a high-fidelity simulation benchmark model of a modified supermarket refrigeration system created in MATLAB and Simulink is modeled using a nonlinear system identification technique. The original model consists of a cold storage room, three open display cases, the suction manifold and the compressor rack. Since open display cases are less energy-efficient, they were removed, while the cold storage room with a door was used for simulation. The suction manifold model has two outputs: the suction pressure and the compressor's power consumption; and it has three inputs: the mass flow of refrigerant, the ambient temperature, and the compressor capacity. A fourteen day simulation was carried out, and synthetic data were generated from the input and output data of the simulation model. These data were divided into estimation data and validation data. Wavelet networks were then utilized to estimate and validate a nonlinear ARX model. The comparison between the estimation data and the validation data shows a goodness of fit that is greater than 88%, with a simulation focus. The data-driven identified model of the suction manifold was stable and robust and could handle strong nonlinearities of the input and output variables when used to replace the Simulink model of the suction manifold subsystem in the simulation benchmark. The simulation results clearly demonstrate how complex refrigeration system subsystems can be replaced with simpler and data-compliant data-driven models.