The Grey Model GM (1, 1) based on the grey system theory has been extensively used as a powerful tool for data forecasting in recent years. In this study, the accuracies of two different grey models include original GM (1, 1) and modified GM (1, 1) using Fourier series have been investigated. So, the performance of these models has been compared with ARIMA as a conventional forecasting model. For this purpose, gold price as a high noisy data has been used. Numerical results was showed that the modified GM (1, 1) provides better performance in model fitting and model forecasting.