[en] System identification is a procedure to characterize the dynamic behavior of a system, a system component based on measured data. This paper presents a study of the modeling and parameter identification of a refrigerator process by using the mathematical black-box modeling technique- ARX and ARMAX structure. A general ARX and ARMAX structure has been constructed for usual thermoelectric refrigerator systems and the Recursive Least Square (RLS) process is used for model parameters identification. The capabilities of the model constructed compared with that of ARX and ARMAX model. Several compositions of ARX and ARMAX orders and forgetting factor are analyzed for thermoelectric air-conditioning model to examine the optimal adjustments that improve their efficiency of PID controller