Introducing new methods to enhance health services for elderly persons has become the main objective of Smart Home researchers. One of the most important issues that they have dealt with is the application of forecasting models used to predict states of elderly persons. In fact, our approach focuses on some critical health parameters (blood pressure, pulse, etc) over 40 days. In this paper, we have applied the forecasting Grey Model GM(1,1) on data collected in the smart home MavHome Project. We have also compared the system performances obtained to predict sensor datawhile using the Grey model with those provided while applying the Box-Jenkins ARIMA as a conventional forecasting model. The simulation results show that the Grey Model is more efficient than the Box-Jenkins ARIMA as it has resulted in more accurate forecasting values.