## 4 Experimental Results
### Multi-Time-Step Prediction Comparisons between Proposed and Benchmark Models
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Look-Back**} & \multirow{2}{*}{**Optimizer**} & \multirow{2}{*}{**Feature**} & \multicolumn{3}{c}{**CNN-LSTM**} & \multicolumn{3}{c}{**GRU-CNN**} & \multicolumn{3}{c}{**Ensemble**} \\ \cline{4-11} \multicolumn{2}{c}{} & & & **DAX** & **DOW** & **S\&P500** & **DAX** & **DOW** & **S\&P500** & **DAX** & **DOW** & **S\&P500** \\ \hline \multirow{8}{*}{5 days} & \multirow{4}{*}{Adam} & MV & 0.1349 & **0.1894** & **0.2386** & 0.0786 & **0.0920** & **0.1012** & 0.1561 & 0.3217 & 0.0551 \\  & & MV & **0.0563** & 0.2293 & 0.3409 & **0.0528** & 0.1421 & 0.1017 & 0.0409 & 0.0781 & 0.0832 \\  & & OHLY & 0.1654 & 0.2088 & 0.2907 & 0.0698 & 0.1321 & 0.1336 & 0.0424 & 0.0583 & 0.0457 \\  & & OHLMVC & 0.1963 & 0.2775 & 0.2648 & 0.0631 & 0.1414 & 0.1085 & **0.0376** & 0.0572 & **0.0427** \\ \cline{2-11} \cline{2-11}  & & MV & 0.1277 & 0.2466 & **0.1705** & 0.0476 & **0.1098** & 0.1520 & 0.0448 & 0.0698 & 0.0569 \\  & & MWSTrop & 0.1008 & **0.1616** & 0.2727 & 0.0472 & 0.1208 & 0.1554 & 0.0429 & 0.1027 & 0.0606 \\  & & OHLY & **0.0868** & 0.1747 & 0.1881 & 0.0525 & 0.1397 & **0.1304** & 0.0447 & **0.0483** & 0.0620 \\  & & OHLMVC & 0.1114 & 0.2308 & 0.2130 & **0.0434** & 0.1452 & 0.1567 & **0.0400** & 0.0531 & **0.0560** \\ \hline \multirow{8}{*}{21 days} & \multirow{4}{*}{Adam} & MV & **0.1679** & **0.198** & 0.3751 & 0.0828 & 0.1555 & **0.0897** & 0.0414 & 0.0603 & 0.2791 \\  & & OHLY & 0.2673 & 0.4012 & 0.4062 & 0.0699 & **0.02929** & 0.1394 & 0.0457 & 0.0770 & 0.0484 \\  & & OHLMVC & 0.1753 & 0.3138 & **0.2623** & 0.0582 & 0.1157 & 0.1363 & 0.0406 & 0.0417 & 0.0483 \\  & & OHLMVC & 0.2692 & 0.4271 & 0.4016 & **0.0546** & 0.1249 & 0.0728 & 0.0396 & **0.0412** & **0.0350** \\ \cline{2-11} \cline{2-11}  & & MV & 0.3389 & 0.2637 & **0.1844** & 0.1218 & 0.1313 & **0.1998** & **0.0421** & 0.0589 & 0.0683 \\  & & MPC & 0.2507 & 0.2386 & 0.2320 & **0.0980** & **0.0982** & 2.2102 & 0.0535 & 0.1073 & 0.0969 \\  & & OHLMVC & 0.2850 & **0.1612** & 0.3277 & 0.0900 & 0.1096 & 0.2077 & 0.0547 & 0.3192 & 0.0671 \\  & & OHLMVC & **0.1878** & 0.3017 & 0.3532 & 0.1293 & 0.1242 & 0.2014 & 0.1280 & **0.0476** & 0.0810 \\ \hline \multirow{8}{*}{42 days} & \multirow{4}{*}{Adam} & MV & **0.1471** & 0.4368 & 0.3548 & 0.1859 & 0.0223 & 0.1943 & 0.0415 & 0.0648 & **0.0476** \\  & & MVC & 0.1884 & 0.2731 & 0.2670 & 0.0921 & 0.1885 & 0.1613 & 0.0616 & 0.3178 & 0.0592 \\  & & OHLMVC & 0.1539 & **0.2643** & **0.1849** & 0.1104 & 0.2039 & **0.1443** & **0.0394** & 0.0725 & 0.0557 \\  & & OHLMVC & 0.2555 & 0.3332 & 0.3816 & **0.0755** & **0.1707** & 0.1935 & 0.0406 & 0.0584 & 0.0753 \\ \cline{2-11} \cline{2-11}  & & MV & **0.2048** & 0.4303 & 0.3616 & 0.0904 & 0.2019 & 0.1691 & 0.0473 & 0.1037 & 0.0786 \\ \cline{2-11}  & & MVC & 0.2602 & 0.5322 & 0.2999 & 0.0744 & **0.1899** & 0.2186 & 0.0445 & 0.3711 & 0.0873 \\ \cline{2-11}  & & OHLMVC & 0.2904 & 0.5066 & 0.3259 & 0.0628 & 0.2044 & **0.1510** & 0.3172 & 0.0683 & **0.0493** \\ \cline{2-11}  & & OHLMVC & 0.2310 & **0.3181** & **0.2358** & **0.0622** & 0.1973 & 0.2204 & **0.0417** & **0.05831** & 0.0657 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of different optimizers and features in terms of average MAE over the three periods for five-time-step prediction. Figure 10: Comparison of true and predicted close prices of the DOW index between different look-back periods for five-time-step prediction over the period from 1 January 2000 through 31 December 2019. Figure 9: Comparison of true and predicted close prices of the DAX index between different look-back periods for five-time-step prediction over the period from 24 October 2014 through 31 December 2019.