The performance of hybrid ARIMA-GARCH modeling in forecasting gold price

Abstract

Gold has been considered a safe return investment because of its characteristic to hedge against inflation. As a result, the models to forecast gold must reflect its structure and pattern. Gold prices follow a natural univariate time series data and one of the methods to forecast gold prices is Box-Jenkins, specifically the autoregressive integrated moving average (ARIMA) models. This is due to its statistical properties, accurate forecasting over a short period of time, ease of implementation and able to handle nonstationary data. Despite the fact that ARIMA is powerful and flexible in forecasting, however it is not able to handle the volatility and nonlinearity that are present in the data series. Previous studies showed that generalized autoregressive conditional heteroskedatic (GARCH) models are used in time series forecasting to handle volatility in the commodity data series including gold prices. Hence, this study investigate the performance of hybridization of potential univariate time series specifically ARIMA models with the superior volatility model, GARCH incorporates with the formula of Box-Cox transformation in analyzing and forecasting gold price. The Box-Cox transformation is used as the data transformation due to its power in normalizing data, stabilizing variance and reducing heteroskedasticity. There is two-phase procedure in the proposed hybrid model of ARIMA and GARCH. In the first phase, the best of the ARIMA models is used to model the linear data of time series and the residual of this linear model will contain only the nonlinear data. In the second phase, the GARCH is used to model the nonlinear patterns of the residuals. This hybrid model which combines an ARIMA model with GARCH error components is applied to analyze the univariate series and to predict the values of approximation. In this procedure, the error term ε t of the ARIMA model is said to follow a GARCH process of orders r and s. The performance of the proposed hybrid model is analyzed by employing similar 40 daily gold price data series used by Asadi et al. (2012), Hadavandi et al. (2010), Khashei et al. (2009) and Khashei et al. (2008). From the plotting in-sample series, the gold price series does not vary in a fixed level which indicates that the series is nonstationary in both mean and variance, exhibits upward and nonseasonal trends which reflect the ARIMA models. The hybridization of ARIMA(1,1,1)-GARCH(0,2) revealed significant result at 1% significance level and satisfied the diagnostic checking including the heteroskedasticity test. The plotting of forecast and actual data exhibited the trend of forecast prices follows closely the actual data including for the simulation part of five days out-sample period. Consequently, the hybrid model of ARIMA(1,1,1)GARCH(0,2) for the transformed data is given by * yt = 0.274 yt*−1 + 0.726 yt*−2 + ε t − 0.992ε t−1, ε t ~ iid N(0,1) σ t2 = 1.16 ×10 −5 + 1.992σ t2−1 − 1.025σ t2−2 Empirical results indicate that the proposed hybrid model ARIMA-GARCH has improved the estimating and forecasting accuracy by fivefold compared to the previously selected forecasting method. The findings suggest that combination of ARIMA (powerful and flexibility) and GARCH (strength of models in handling volatility and risk in the data series) have potential to overcome the linear and data limitation in the ARIMA models. Thus, this hybridization of ARIMA-GARCH is a novel and promising approach in gold price modeling and forecasting.