## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Look-Back Period**} & \multirow{2}{*}{**Metric**} & \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**One-Time-Step Prediction**} & \multicolumn{3}{c}{**Five-Time-Step Prediction**} \\ \cline{4-9}  & & & **DAX** & **DOW** & **S\&P500** & **DAX** & **DOW** & **S\&P500** \\ \hline \multirow{9}{*}{5 days} & \multirow{9}{*}{MSE} & RNN & 0.1738 & 0.3059 & 0.1043 & 0.0250 & 0.0219 & 0.1122 \\  & & LSTM & 0.1735 & 0.3060 & 0.1043 & **0.0058** & **0.0076** & 0.0064 \\  & & GRU & 0.1735 & 0.3060 & 0.1043 & 0.0081 & 0.0187 & 0.0058 \\  & & WaveNet & 0.4870 & 0.3120 & 0.5712 & 0.0477 & 0.1230 & 0.0177 \\  & & CNN-LSTM & 0.1435 & 0.0560 & 0.0988 & 0.0831 & 0.0447 & 0.0912 \\  & & GRU-CNN & 0.0370 & 0.3060 & 0.0053 & 0.0101 & 0.0166 & 0.0090 \\  & & Ensemble & **0.0017** & **0.0051** & **0.0027** & 0.0126 & 0.0122 & **0.0057** \\ \hline \multirow{9}{*}{5 days} & \multirow{9}{*}{MAE} & RNN & 0.3738 & 0.5163 & 0.2934 & 0.1468 & 0.1266 & 0.3053 \\  & & LSTM & 0.3726 & 0.5165 & 0.2934 & **0.0593** & **0.0640** & **0.0585** \\  & & GRU & 0.3727 & 0.5164 & 0.2934 & 0.0802 & 0.1251 & 0.0629 \\  & & WaveNet & 0.6741 & 0.5185 & 0.7456 & 0.1925 & 0.3177 & 0.1110 \\  & & CNN-LSTM & 0.3440 & 0.1587 & 0.2864 & 0.2345 & 0.1551 & 0.2666 \\  & & GRU-CNN & 0.1733 & 0.5165 & 0.0557 & 0.0901 & 0.1139 & 0.0739 \\  & & Ensemble & **0.0345** & **0.0628** & **0.0420** & 0.1025 & 0.0968 & 0.0605 \\ \hline \multirow{9}{*}{21 days} & \multirow{9}{*}{MSE} & RNN & 0.1787 & 0.3315 & 0.0995 & 0.1917 & 0.3485 & 0.1081 \\  & & LSTM & 0.1785 & 0.3315 & 0.0995 & 0.0133 & **0.0070** & 0.0060 \\  & & GRU & 0.1785 & 0.3315 & 0.0995 & 0.0126 & 0.0155 & **0.0056** \\  & & WaveNet & 0.4126 & 0.2232 & 0.5259 & 0.0526 & 0.1446 & 0.0177 \\  & & CNN-LSTM & 0.0805 & 0.0225 & 0.0680 & 0.0399 & 0.0127 & 0.0595 \\  & & GRU-CNN & 0.0159 & 0.0307 & 0.0058 & 0.0245 & 0.0127 & 0.0079 \\  & & Ensemble & **0.0018** & **0.0128** & **0.0026** & **0.0115** & 0.0124 & 0.0059 \\ \hline \multirow{9}{*}{21 days} & \multirow{9}{*}{MAE} & RNN & 0.3947 & 0.5588 & 0.2950 & 0.4151 & 0.5807 & 0.3127 \\  & & LSTM & 0.3940 & 0.5588 & 0.2950 & 0.1019 & **0.0645** & **0.0625** \\  & & GRU & 0.3940 & 0.5587 & 0.2950 & 0.1032 & 0.1121 & 0.0634 \\  & & WaveNet & 0.6244 & 0.4501 & 0.7168 & 0.2015 & 0.3605 & 0.1094 \\  & & CNN-LSTM & 0.2490 & 0.1076 & 0.2367 & 0.1460 & 0.0808 & 0.2231 \\  & & GRU-CNN & 0.1133 & 0.1626 & 0.0634 & 0.1429 & 0.0994 & 0.0678 \\  & & Ensemble & **0.0358** & **0.1027** & **0.0402** & **0.0966** & 0.0980 & 0.0650 \\ \hline \multirow{9}{*}{42 days} & \multirow{9}{*}{MSE} & RNN & 0.2434 & 0.4011 & 0.1446 & 0.0481 & 0.0071 & 0.1150 \\  & & LSTM & 0.2434 & 0.4011 & 0.1446 & **0.0071** & 0.0040 & 0.0066 \\  & & GRU & 0.2434 & 0.4011 & 0.1446 & 0.0079 & 0.0122 & **0.0044** \\  & & WaveNet & 0.3106 & 0.1505 &Further, compared with other forecasting methods in other fields, the proposed framework herein can be applied to forecasting time-series data, such as energy consumption, oil price, gas concentration, air quality, and river flow. Moreover, the performance of forecasting can be improved by combining different types of RNN-based models and constructing a portfolio using predicted stock market prices in future studies.