# Forecasting Steel Production in the World--Assessments Based on Shallow and Deep Neural Networks
## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Window** & **Gap** & **MLP** & **LSTM** & **GRU** & **CNNMLP** & **CNNLSTM** & **CNNGRU** \\ \hline \multirow{8}{*}{4} & 1 & **4.54** & 5.18 & 4.67 & 4.75 & 5.9 & 5.59 \\  & 2 & 6.93 & 7.5 & 7.99 & 7.29 & 7.57 & 6.93 \\  & 3 & 9.84 & 10.12 & 9.66 & 9.0 & 8.67 & 9.67 \\  & 4 & 10.77 & 11.91 & 11.55 & 10.82 & 10.06 & 10.49 \\  & 5 & 12.7 & 13.97 & 12.76 & 13.06 & 11.74 & 12.09 \\  & 6 & 14.15 & 15.24 & 13.44 & 13.05 & 13.36 & 12.84 \\  & 7 & 15.77 & 16.76 & 16.24 & 15.09 & 14.44 & 15.74 \\  & 8 & 18.78 & 18.08 & 18.23 & 17.35 & 15.96 & 19.54 \\ \hline \multirow{8}{*}{6} & 1 & 5.65 & 4.86 & 4.85 & **4.73** & 5.56 & 6.89 \\  & 2 & 9.42 & 8.94 & 7.71 & 7.87 & 9.16 & 9.12 \\  & 3 & 10.04 & 10.38 & 9.17 & 9.68 & 10.76 & 11.18 \\  & 4 & 11.97 & 11.46 & 10.49 & 10.55 & 9.43 & 11.49 \\  & 5 & 12.97 & 12.5 & 12.1 & 10.84 & 11.27 & 11.13 \\  & 6 & 14.03 & 14.17 & 14.21 & 14.52 & 12.23 & 10.55 \\  & 7 & 15.71 & 15.82 & 16.0 & 14.01 & 12.42 & 11.81 \\  & 8 & 17.46 & 16.81 & 18.23 & 16.24 & 20.43 & 15.6 \\  & 1 & 5.85 & 5.11 & 5.23 & **4.59** & 4.85 & 5.52 \\  & 2 & 8.62 & 9.54 & 7.18 & 6.82 & 6.21 & 7.16 \\  & 3 & 10.03 & 10.29 & 9.71 & 10.32 & 7.3 & 7.58 \\  & 4 & 11.89 & 11.06 & 10.63 & 11.71 & 6.71 & 7.63 \\  & 5 & 11.62 & 14.9 & 12.2 & 11.26 & 10.79 & 8.71 \\  & 6 & 14.37 & 14.39 & 13.84 & 12.03 & 12.55 & 15.48 \\  & 7 & 15.46 & 14.63 & 15.3 & 18.41 & 6.22 & 9.3 \\  & 8 & 17.88 & 15.46 & 17.13 & 15.17 & 7.88 & 6.35 \\ \hline \multirow{8}{*}{10} & 1 & 5.61 & **5.02** & 5.09 & 5.46 & 5.06 & 5.41 \\  & 2 & 9.74 & 14.0 & 7.73 & 7.03 & 6.59 & 7.16 \\  & 3 & 9.66 & 10.88 & 9.44 & 9.96 & 7.35 & 8.11 \\  & 4 & 10.67 & 11.78 & 12.35 & 10.19 & 7.99 & 11.23 \\  & 5 & 12.6 & 14.67 & 13.81 & 10.96 & 12.42 & 12.07 \\  & 6 & 13.11 & 13.78 & 13.58 & 10.96 & 9.72 & 16.83 \\  & 7 & 14.43 & 15.57 & 14.47 & 13.0 & 16.32 & 11.52 \\  & 8 & 15.05 & 16.14 & 17.25 & 16.15 & 8.81 & **4.82** \\ \hline \multirow{8}{*}{12} & 1 & **5.28** & 7.33 & 5.74 & 5.59 & 5.42 & 5.66 \\  & 2 & 7.84 & 10.03 & 8.77 & 8.48 & 5.61 & 9.4 \\  & 3 & 10.2 & 11.14 & 10.36 & 10.66 & 9.13 & 8.96 \\  & 4 & 9.56 & 13.64 & 12.02 & 9.71 & 11.11 & 11.14 \\  & 5 & 9.92 & 13.13 & 12.01 & 11.98 & 13.51 & 14.32 \\  & 6 & 11.69 & 13.66 & 12.17 & 10.89 & 13.35 & 18.05 \\  & 7 & 17.06 & 17.13 & 15.76 & 12.62 & 16.6 & 27.02 \\  & 8 & 14.25 & 14.22 & 16.95 & 18.39 & 12.83 & 23.63 \\ \hline \multirow{8}{*}{14} & 1 & 5.69 & 5.71 & 5.5 & 6.13 & **4.31** & 6.31 \\  & 2 & 8.89 & 12.5 & 8.65 & 7.99 & 10.84 & 10.35 \\  & 3 & 11.3 & 11.88 & 8.86 & 9.06 & 12.64 & 14.12 \\  & 4 & 11.25 & 12.83 & 11.89 & 9.26 & 14.58 & 13.7 \\  & 5 & 14.51 & 10.34 & 12.58 & 10.59 & 13.47 & 15.48 \\  & 6 & 11.35 & 14.93 & 9.6 & 10.02 & 13.37 & 13.88 \\  & 7 & 15.73 & 14.47 & 12.37 & 12.4 & 14.09 & 15.97 \\  & 8 & 15.77 & 11.62 & 13.67 & 13.47 & 16.4 & 30.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MAPE errors of tests with different historical windows (4–14 samples) and gaps (years ahead) ranging from 1 to 8.  
models. The convolutional layer seems to offer some stability in the LSTM and GRU models for midterm predictions, when historical windows of 10-12 samples are used.