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

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

A hybrid model for improving Malaysian gold forecast accuracy

A hybrid model has been considered an effective way to improve forecast accuracy. This paper proposes the hybrid model of the linear autoregressive moving average (ARIMA) and the non-linear generalized autoregressive conditional heteroscedasticity (GARCH) in modeling and forecasting. Malaysian gold price is used to present the development of the hybrid model. The goodness of fit of the model is measured using Akaike information criteria (AIC) while the forecasting performance is assessed using bias, variance proportion, covariance proportion and mean absolute percentage error (MAPE)

Symmetric and asymmetric garch models for forecasting the prices of gold

Gold prices forecasts are of interest to many people. Gold prices however, change rapidly from period to period. In short, they are not constant. The change is not only in the mean, but also in the variability of the gold prices series. Daily gold prices per ounce, from January 3, 2000 to December 31, 2010 is used in this study with the Schwarz Information Criterion (SIC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) as the forecasting accuracy measures. For the purpose of this study, gold prices from ten major consumer countries are examined. The currencies are American dollar, Australian dollar, Canadian dollar, Swiss franc, Chinese renmimbi, Egyptian pound, Euro, Japanese yen, Turkish lira and South African rand. This study considers five models from the GARCH-family namely the Generalized Autoregressive Conditional Heteroscedasticity (GARCH (p, q)), GARCH-M, Power of GARCH (PGARCH), Threshold GARCH (TGARCH) and Exponential GARCH (EGARCH). These models are analyzed by using the E-Views 6.0 software. Several combinations of p and q values are considered to develop several GARCH (p, q) models. Using the maximum likelihood method to estimate the coefficients in the models, followed by model validation and model selection criteria, it is concluded that EGARCH (1, 1) and TGARCH (1, 1) are the best models for eight of the currencies understudied

Symmetric and asymmetric garch models for forecasting the prices of gold

Gold prices forecasts are of interest to many people. Gold prices however, change rapidly from period to period. In short, they are not constant. The change is not only in the mean, but also in the variability of the gold prices series. Daily gold prices per ounce, from January 3, 2000 to December 31, 2010 is used in this study with the Schwarz Information Criterion (SIC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) as the forecasting accuracy measures. For the purpose of this study, gold prices from ten major consumer countries are examined. The currencies are American dollar, Australian dollar, Canadian dollar, Swiss franc, Chinese renmimbi, Egyptian pound, Euro, Japanese yen, Turkish lira and South African rand. This study considers five models from the GARCH-family namely the Generalized Autoregressive Conditional Heteroscedasticity (GARCH (p, q)), GARCH-M, Power of GARCH (PGARCH), Threshold GARCH (TGARCH) and Exponential GARCH (EGARCH). These models are analyzed by using the E-Views 6.0 software. Several combinations of p and q values are considered to develop several GARCH (p, q) models. Using the maximum likelihood method to estimate the coefficients in the models, followed by model validation and model selection criteria, it is concluded that EGARCH (1, 1) and TGARCH (1, 1) are the best models for eight of the currencies understudied

Forecasting Malaysian gold using a hybrid of ARIMA and GJR-GARCH models

An effective way to improve forecast accuracy is to use a hybrid model. This paper proposes a hybrid model of linear autoregressive moving average (ARIMA) and non-linear GJR-GARCH model also known as TARCH in modeling and forecasting Malaysian gold. The goodness of fit of the model is measured using Akaike information criteria (AIC) while the forecasting performance is assessed using mean absolute percentage error (MAPE), bias proportion, variance proportion and covariance proportio

A Hybrid Model for Improving Malaysian Gold Forecast Accuracy

A hybrid model has been considered an effective way to improve forecast accuracy. This paper proposes the hybrid model of the linear autoregressive moving average (ARIMA) and the non-linear generalized autoregressive conditional heteroscedasticity (GARCH) in modeling and forecasting. Malaysian gold price is used to present the development of the hybrid model. The goodness of fit of the model is measured using Akaike information criteria (AIC) while the forecasting performance is assessed using bias, variance proportion, covariance proportion and mean absolute percentage error (MAPE)