# Forecasting Daily Temperatures with Different Time Interval Data Using Deep Neural Networks
## 4 Data
### Experimental Results  
To check the significance of the forecasting performance, we performed the experiments 25 times for each setting with random initialization of model weights. Tables 15-17 show the mean MAEs with standard deviations for each setting and each of the three regions for the average, minimum, and maximum temperature forecasts. For instance, when we predicted the minimum temperature in Seoul 25 times using three-day time unit data, the mean and standard deviation for the MAE were 1.246 and 0.041, respectively. To aid in understanding, Figures 4-6 show box plots of the best performance among the different input time lengths for each setting with the boldfaced values in Tables 15-17. We explain the experimental results for each factor as follows. First, for model structures, the CNN performed best with both daily and hourly input data; in the metropolitan area using hourly input data, the CNN showed means of MAE 1.295, 1.246, and 2.001 for average, minimum, and maximum temperature, respectively. MLP showed averages MAEs of 1.344, 1.353, and 2.065, and the LSTM averages of MAE were 1.380, 1.299, and 2.055, both respectively. The standard deviations were 0.029, 0.041, and 0.022 for the CNN; 0.027, 0.024, and 0.037 for the MLP, and 0.181, 0.087, and 0.130 for the LSTM; the LSTM showed larger standard deviations than those with the CNN and MLP. As Figure 4 shows, the first quartiles of LSTM using hourly input data are lower than those of the MLP using the same data. However, the gap between the first and third LSTM quartiles was large, and there were a few outliers. In contrast, the CNN showed robust performance in both means and standard deviations. In terms of time units of the input data, the hourly data showed better performance than did the daily data. In particular, the difference was prominent when forecasting average and minimum temperatures. In Figures 4-6, the box plots show that the first quartiles of results using daily input data are higher than the third quartiles of results using hourly data. For time length of input data, based on the results boldfaced in Tables 15-17, the best results were 22 times for 1 day, 11 times for 3 days, 14 times for 5 days, 5 times for 10 days, and 2 times for 30 days. We obtained most of the best results when the length of the input data ranged from 1 to 5 days. However, it was interesting to note that the LSTM model showed the best results when we used longer input data, and the MLP showed the best results with short data lengths. With the CNN, hourly input data, and forecasting the coastal area, longer input data showed the best performance. In contrast, shorter input data were best for forecasting in the mountainous area. Therefore, the time length of the input data can be interpreted to be affected not only by the artificial neural network model but also by the region. Overall, the models performed best in Seongsan, the coastal area, and the worst in Daegwallyeong, the mountainous area. The forecasting performance best to worst was for the coastal area, the metropolitan area, and then the mountainous area. With the CNN with hourly input data, the best average MAEs for the coastal area were 1.210, 1.234, and 1.900, and the best averages for the mountainous area were 1.481, 1.700, and 2.367. Therefore, the differences in forecasting accuracy across regions are apparent in each region. For the three temperatures, we forecasted, predicting the maximum temperature was obviously the most difficult task. In Tables 15-17, all maximum temperatures under the same setting give worse results than those for the average and minimum temperatures. We found a clear pattern in the experimental results that predicting the maximum temperatures in the mountainous area was difficult, and we interpreted the causes of these results as follows. Table 18 shows the daily differences in temperatures between yesterday and today for 10 years, called differencing.