A GARCH model selection and estimation method based on neural network with the loss function of mean square error and model confidence set

This paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back-propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p-value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p-value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p-value of MCS of the best model estimated by this method is higher than the p-value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p-value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.