# Hybrid Forecasting Models Based on the Neural Networks for the Volatility of Bitcoin
## 3 Hybrid Models and Results  
In this paper, we propose several hybrid models based on GARCH family models, ANN and HONN to find a more accurate model for forecasting of Bitcoin volatility. Specifically, the hybrid models are constructed with the ANN by using the selected GARCH models and the selected explanatory variables. The models are implemented by the ANN with a single hidden layer and various neurons using the back-propagation method and classified according to whether including the explanatory variables or not. The proposed models are used for 1-day ahead forecast of weekly realized volatility, and then the best model is determined by comparing the results. We compare the proposed models to find the best volatility forecasting model in the bitcoin market. We first forecast the volatility of Bitcoin price using the classic GARCH family models. Concretely, we use GARCH, EGARCH and GJR-GARCH model among the GARCH family models and the \((p,q)\) parameters ranging from (1,1) to (3,3). In order to find the optimal GARCH model for the hybrid model, we provide AIC and BIC values in Table 2 and three measures to compare the performances of the models for forecasting volatilities in Table 3. According to the results in Table 2 and AIC and BIC criteria, EGARCH(3,3) model is the best model. On the other hand, according to the results in Table 3, we can see that the GJR-GARCH(1,1) model performs the best among the introduced GARCH family models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & \(\boldsymbol{(p,q)}\) & **AIC** & **BIC** \\ \hline GARCH & (1,1) & \(-7593.56\) & \(-7570.83\) \\ GARCH & (2,2) & \(-7633.38\) & \(-7599.30\) \\ GARCH & (3,3) & \(-7630.73\) & \(-7585.28\) \\ GJR-GARCH & (1,1) & \(-7589.75\) & \(-7561.34\) \\ GJR-GARCH & (2,2) & \(-7577.91\) & \(-7538.14\) \\ GJR-GARCH & (3,3) & \(-7558.42\) & \(-7507.29\) \\ EGARCH & (1,1) & \(-7646.91\) & \(-7618.51\) \\ EGARCH & (2,2) & \(-7665.96\) & \(-7626.19\) \\ EGARCH & (3,3) & \(-7687.68\) & \(-7636.55\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: GARCH models. Figure 6: Lagged volatility \(LV_{t}\) of \(r_{t}\) from 1 January 2012 to 30 November 2019. Other models except for the classic GARCH models are based upon the ANN approach or the HONN approach. In other words, the models are constructed by using the selected input variables to ANN or HONN. Similar to [31; 34], we propose the ANN-GARCH models for the forecasting of the Bitcoin volatility using the outputs of the GARCH family models. Specifically, we define the GT-GARCH model and GT-VIX-GARCH model according to the input variables. The input variables of the models are in Table 4. In order to find the optimal number of nodes in the hidden layer and the activation function for the models, we carry out the experiments using the Adam optimizer method [49] to update the network weights. The results are indicated with four activation functions in Tables 5 and 6. As shown in Tables 5 and 6, two measures (MAE, RMSE) show that the GT-GARCH model is better than the GT-VIX-GARCH model, and one measure (MAPE) shows a different result. From these results, we can not find a significant performance difference between the GT-VIX-GARCH model and the GT-GARCH model. That is, we conclude that two models may have a similar predictive ability. To improve the accuracy of the model, we adopt the HONN approach. Specifically, we propose three types of hybrid models (GT-H model, GT-VIX-H model, GT-VIX-GARCH-H model) based on the HONN. Tables 7-9 are presented the results of the models based on the HONN. To examine well the proposed models based on the HONN, we present a summary of the input variables of each model in Table 10. In Table 10, '\(LV_{t}\)' is in Equation (6), 'GT' means Google trends data, 'VIX' means VIX index data, 'GJR-GARCH(1,1)' means forecast by GJR-GARCH(1,1) and 'EGARCH(3,3)' means forecast by EGARCH(3,3).