# Hybrid Forecasting Models Based on the Neural Networks for the Volatility of Bitcoin
## 3 Hybrid Models and Results
Tables 7 and 8 present the results of the HONN model without the outputs of GARCH models as shown in Table 10. We can see that MAE and MAPE in Tables 7 and 8 increase in all cases as compared to the values in Tables 5 and 6. That is, GT-H model and GT-VIX-H model do not show better performance compared to the models based on the ANN. To improve the model, we adopt the HONN model with the outputs of GARCH family models. Among the introduced GARCH models, we chose GJR-GARCH(1,1) and EGARCH(3,3) from the results in Tables 2 and 3. By using the outputs of GJR-GARCH(1,1) and EGARCH(3,3) as input variables in the HONN, we finally construct and propose a new type of hybrid model (GT-VIX-GARCH-H model) for better forecasting of Bitcoin volatility. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Activation Function** & **Nodes** & **MAE** & **RMSE** & **MAPE** \\ \hline GT-VIX-GARCH & Relu & 10 & 0.016464618 & 0.022961953 & 43.6754142 \\  & & 20 & 0.016463169 & 0.022961503 & 43.66309023 \\  & & 30 & 0.016464239 & 0.022963376 & 43.66271481 \\  & & 40 & 0.016464096 & 0.022965466 & 43.65610286 \\  & & 50 & 0.016468159 & 0.022966994 & 43.68492065 \\ \hline  & Tanh & 10 & 0.016465239 & 0.022964124 & 43.67126798 \\  & & 20 & 0.016463913 & 0.022960066 & 43.67926114 \\  & & 30 & 0.016464939 & 0.022962888 & 43.67179649 \\  & & 40 & 0.01646529 & 0.022962936 & 43.68079538 \\  & & 50 & 0.016463781 & 0.022958457 & 43.68308928 \\ \hline  & Elu & 10 & 0.016464796 & 0.022964955 & 43.66256389 \\  & & 20 & 0.016465883 & 0.02296502 & 43.67128545 \\  & & 30 & 0.016464635 & 0.022962084 & 43.67544449 \\  & & 40 & 0.016466452 & 0.022966505 & 43.66998111 \\  & & 50 & 0.016462585 & 0.022957731 & 43.67119374 \\ \hline  & Sigmoid & 10 & 0.01646477 & 0.022963578 & 43.67003712 \\  & & 20 & 0.016461495 & 0.022957864 & 43.67131767 \\  & & 30 & 0.016464624 & 0.022961432 & 43.67831534 \\  & & 40 & 0.016464975 & 0.022965387 & 43.66149144 \\  & & 50 & 0.01647861 & 0.02302727 & 43.4274305 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: GT-VIX-GARCH model performance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Activation Function** & **Nodes** & **MAE** & **RMSE** & **MAPE** \\ \hline GT-GARCH & Relu & 10 & 0.016455061 & 0.0228628 & 44.03939302 \\  & & 20 & 0.016455761 & 0.02286762 & 44.01794052 \\  & & 30 & 0.016456899 & 0.022870071 & 44.01377941 \\  & & 40 & 0.016457765 & 0.02287134 & 44.01490369 \\  & & 50 & \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Activation Function** & **Nodes** & **MAE** & **RMSE** & **MAPE** \\ \hline GT-H & Relu & 10 & 0.016941584 & 0.022027929 & 52.70636488 \\  & & 20 & 0.016941599 & 0.02202816 & 52.70680583 \\  & & 30 & 0.016941163 & 0.022027678 & 52.70298093 \\  & & 40 & 0.016940914 & 0.022027074 & 52.70274993 \\  & & 50 & 0.016941279 & 0.022027853 & 52.70347102 \\ \hline  & Tanh & 10 & 0.016941714 & 0.022027935 & 52.70708064 \\  & & 20 & 0.016942079 & 0.022028228 & 52.70821739 \\  & & 30 & 0.016941977 & 0.022028122 & 52.70722389 \\  & & 40 & 0.016941485 & 0.022028033 & 52.70475844 \\  & & 50 & 0.016940999 & 0.022027369 & 52.70261778 \\ \hline  & Elu & 10 & 0.01694181 & 0.022028066 & 52.70750404 \\  & & 20 & 0.016941503 & 0.022027574 & 52.70587155 \\  & & 30 & 0.016942019 & 0.022027821 & 52.7097488 \\  & & 40 & 0.01694203 & 0.022027968 & 52.70826475 \\  & & 50 & 0.01694185 & 0.022027961 & 52.71021157 \\ \hline  & Sigmoid & 10 & 0.016941511 & 0.022027945 & 52.70543218 \\  & & 20 & 0.016941295 & 0.022027628 & 52.70568077 \\  & & 30 & 0.016941514 & 0.022028015 & 52.70581447 \\  & & 40 & 0.016942199 & 0.022028407 & 52.70889483 \\  & & 50 & 0.016941966 & 0.022027852 & 52.70746498 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: GT-H model performance.