# DERN: Deep Ensemble Learning Model for Short- and Long-Term Prediction of Baltic Dry Index
## 4 Experiments
### Long-Term Prediction
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Portion** & **Accuracy Measure** & **Model** & \(t_{1}\) & \(t_{2}\) & \(t_{3}\) & \(t_{4}\) & \(t_{5}\) \\ \hline \multirow{8}{*}{70–30\%} & & ARIMA & 731.07 & 799.10 & 999.08 & 1009.98 & 1020.05 \\  & & MLP & 145.10 & 209.31 & 241.97 & 255.06 & 259.99 \\  & & Deep RNN & 91.96 & 160.28 & 214.43 & 257.35 & 290.34 \\  & & LSTM & 79.40 & 142.33 & 201.69 & 248.45 & 293.33 \\  & & GRU & 79.92 & 155.84 & 219.02 & 276.65 & 325.09 \\  & & DERN & **75.11** & **139.05** & **200.15** & **245.23** & **293.31** \\ \hline \multirow{8}{*}{70–30\%} & & ARIMA & 698.81 & 772.81 & 952.69 & 978.01 & 981.97 \\  & & MLP & 94.92 & 158.19 & 191.09 & 201.44 & 210.03 \\  & & Deep RNN & 64.38 & 111.64 & 153.25 & 188.69 & 214.41 \\  & & LSTM & 58.09 & 99.40 & 141.41 & 180.80 & 212.31 \\  & & GRU & **57.54** & 108.50 & 154.50 & 198.63 & 231.78 \\  & & DERN & 57.90 & **99.00** & **136.03** & **178.81** & **212.05** \\ \hline \multirow{8}{*}{RMSE} & & ARIMA & 100.01 & 121.18 & 141.03 & 152.87 & 164.09 \\  & & MLP & 17.93 & 19.08 & 23.93 & 27.87 & 29.65 \\  & & Deep RNN & 9.46 & 13.19 & 19.30 & 25.75 & 27.46 \\  & & LSTM & 5.73 & 10.86 & 15.90 & 19.64 & 22.89 \\  & & GRU & 5.58 & 10.62 & 15.17 & 19.51 & 22.95 \\  & & DERN & **4.95** & **9.85** & **12.96** & **17.00** & **19.32** \\ \hline \multirow{8}{*}{80–20\%} & & ARIMA & 724.03 & 842.92 & 1000.80 & 1010.75 & 1024.62 \\  & & MLP & 155.29 & 197.45 & 309.62 & 320.74 & 350.97 \\  & & Deep RNN & 98.81 & 138.35 & 167.67 & 212.59 & 224.87 \\  & & LSTM & 67.56 & 122.51 & **160.39** & 190.65 & 213.23 \\  & & GRU & 62.96 & 119.82 & 160.87 & 191.39 & 214.23 \\  & & DERN & **62.04** & **118.98** & 160.99 & **190.01** & **210.00** \\ \hline \multirow{8}{*}{80–20\%} & & ARIMA & 900.17 & 1005.21 & 1042.33 & 1050.39 & 1072.11 \\  & & MLP & 73.48 & 201.08 & 218.01 & 240.55 & 255.12 \\  & & Deep RNN & 60.96 & 104.67 & 129.80 & 167.03 & 179.80 \\  & & LSTM & 53.18 & 92.75 & 137.85 & 151.54 & 171.19 \\  & & GRU & 49.10 & 88.78 & 122.20 & 148.33 & 170.18 \\  & & DERN & **48.56** & **87.39** & **121.76** & **144.72** & **170.00** \\ \hline \multirow{8}{*}{MAPE} & & ARIMA & 123.31 & 143.18 & 183.83 & 189.11 & 192.99 \\  & & MLP & 19.18 & 26.17 & 35.41 & 37.11 & 39.98 \\  & & Deep RNN & 9.07 & 14.24 & 20.76 & 24.53 & 27.81 \\  & & LSTM & 6.93 & 11.87 & 17.74 & 20.26 & 23.93 \\  & & GRU & **6.54** & 10.98 & 16.94 & 19.39 & 21.48 \\  & & DERN & 6.50 & **8.81** & **14.17** & **16.98** & **19.52** \\ \hline \multirow{8}{*}{RMSE} & & ARIMA & 890.01 & 1042.12 & 1370.07 & 1490.10 & 1640.97 \\  & & MLP & 126.39 & 207.45 & 259.11 & 298.55 & 301.54 \\  & & Deep RNN & 93.99 & 137.53 & 166.94 & 175.15 & 221.83 \\  & & LSTM & 71.00 & 131.49 & 178.91 & 216.40 & 241.35 \\  & & GRU & 70.43 & 127.65 & 172.92 & 210.40 & 243.12 \\  & & DERN & **67.29** & **127.51** & **168.92** & **209.55** & **240.76** \\ \hline \multirow{8}{*}{90–10\%} & & ARIMA & 991.47 & 1402.21 & 1707.09 & 1811.87 & 1991.08 \\  & & MLP & 118.22 & 197.53 & 216.10 & 223.09 & 245.12 \\ \cline{1-1}  & & Deep RNN & 58.25 & 98.50 & 132.02 & 162.15 & 182.85 \\ \cline{1-1}  & & LSTM & 55.67 & 103.69 & 142.64 & 174.16 & **194.45** \\ \cline{1-1}  & & GRU & 56.07 & **102.74** & 139.42 & 172.02 & 205.66 \\ \cline{1-1}  & & DERN & **55.61** & 101.19 & **135.19** & **171.04** & 200.11 \\ \hline \multirow{8}{*}{MAPE} & & ARIMA & 124.01 & 189.08 & 231.10 & 256.98 & 279.14 \\ \cline{1-1}  & & MLP & 18.35 & 27.91 & 36.04 & 39.43 & 42.76 \\ \cline{1-1}  & & Deep RNN & 8.99 & 13.98 & 20.28 & 25.15 & 28.20 \\ \cline{1-1}  & & LSTM & 6.73 & 11.95 & 16.01 & 22.25 & 24.06 \\ \cline{1-1}  & & GRU & 6.88 & 10.97 & 17.90 & 20.21 & 25.67 \\ \cline{1-1}  & & DERN & **5.01** & **9.13** & **14.87** & **17.02** & **19.09** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results of five-steps-ahead prediction of BDI.