A hybrid of bekk garch with neural network for modeling and forecasting time series

Abstract

Gold prices change rapidly from time to time. The change is not only in the mean, but also in the variability of the series. The Malaysian Kijang Emas (MKE) is the official national bullion gold coin of Malaysia and it is high in demand. The purchase and resale prices of MKE are determined by the prevailing international gold market price. However, the value of Ringgit Malaysia (RM) that is used to purchase MKE is affected by United States (U.S.) dollar. Thus, the purpose of this study is to develop the best model for forecasting international gold prices, U.S. dollar index and MKE prices by investigating their co-movement. In an attempt to find the best model, fifteen years of data for MKE prices, international gold prices in U.S. dollar and U.S. dollar index were used. This study initially considered three standard methods namely bivariate generalized autoregressive conditional heteroskedasticity (GARCH), trivariate GARCH and multilayer feed-forward neural network (MFFNN). Bivariate and trivariate GARCH are from Baba-Engle-Kraft-Kroner (BEKK) GARCH. The current study further hybridized these methods to improve forecasting accuracy. Bivariate and trivariate GARCH were used to examine the relationship between gold prices and U.S. dollar. The trivariate GARCH was modified to develop GARCH-in-mean model due to the existence risk that was expected in the data. Analysis was done by using E-Views software. However, analysis using MFFNN model and hybridized models were carried out using MATLAB software. Analyses of performances were evaluated using mean absolute percentage error (MAPE) and mean square error (MSE). The MAPE for all in and out sample forecasts were less than 1%. The lowest values of MAPE were 0.8% for gold prices and 0.2% for U.S. dollar index. These low values were produced by using trivariate GARCH-in-mean model that was developed by the current study either as a single or hybdridized model with MFFNN. MSE recorded the values when trivariate GARCH-in-mean model was hybridized with MFFNN using 15 hidden nodes.