Comparison between GM(3,1) forecasting model and Fourier analysis on the problem of air temperatures

Air temperature is one of the climates that needs to be observed for various purposes so that there is a need for forecasting to facilitate use. Air temperature data is in the form of fluctuations that are suitable for use with several forecasting methods, one of which is Grey Forecasting. In addition, to forecast air temperature can also use Fourier Analysis by finding the value of the period and the results of air temperature prediction. So in this study the forecasting used is Grey Forecasting model and Fourier Analysis. This study aims to compare the accuracy of the two methods to determine which is more accurate between the two in air temperature prediction. The Grey Forecasting model used is GM(3,1) using a differential equation 3-order (third) and 1 (one) variable. Meanwhile, Fourier Analysis uses Fast Fourier Transform to determine the period and approximation of the Fourier Series for air temperature forecasting. Based on the calculation using Fast Fourier Transform, the air temperature period at the Karakates Observation Post, Malang Regency from 2015 to 2021 of 10.5≈11 months with an approximation of Fourier Series is 1-order. Furthermore, by using MAPE to determine the error of GM(3,1), a MAPE value of 3.3161 ×105 was obtained in the seventh-eleven data of air temperature and of 1.3690 × 1022 for the entire air temperature data. Because the error of the GM(3,1) > 50% can be categorized as weak and inaccurate forecasting. Meanwhile, the error in the Fourier Analysis was 2.6331 in the seventh-11 (eleven) data and 4.9756 for all air temperature data. This means that the error of Fourier Analysis is less than 10% then it can be categorized as a forecast with a high degree of accuracy. Thus, the best accuracy of the two the method is The Fourier Analysis.