Usually, commercial control solutions for superheat control still use PID controllers as a standard. Although there are several applications of advanced control in refrigeration processes in the literature, there isn't a consensus about the optimal control solution for each system. The implementation of advanced control algorithms ultimately depends on accurate process knowledge in the form of dynamic mathematical models. This study aims to take a first step toward the designing an adaptive stochastic MPC controller for superheat control in an R404 refrigeration cycle with electronic expansion valve by developing stochastic dynamic models of the process. Both time-varying and time-invariant versions of the models are identified. Statistical validation results show whitening of the residuals of the time-invariant models, creating a basis for comparison. The recursive estimation of the time-varying parameters was realized with the Kalman Filter and the Forgetting Factor algorithms. Results of validation tests by simulation show good results, with average output errors between 0.05 and 1.39 degrees C, indicating that the ARMAX with time-varying parameters may be a good presentation for this system. (C) 2017 Elsevier Ltd and IIR. All rights reserved.