Interval Forcasting for Gold Price with hybrib model of ARIMA and Artificial Neural Network

Price forecasting is one of the most challenging issues that the speculators, traders and brokers are faced with. On the other hand in interval analysis it is supposed that observations and estimations in the real world are not complete and reliable so to increase the accuracy we should describe the data as the intervals that includes real quantities. Various methods are used in order to model the time series such as price. Autoregressive integration moving average (ARIMA), which is known as box-Jenkins method is one of the most commonly used models in forecasting of time series during the past three decades. But the main assumption is that there is a linear relationship between the values of the series therefore nonlinear relationships cannot be explained completely by using autoregressive integration moving average (ARIMA). Another method in time series forecasting is neural network which can estimate the various nonlinear relationship (called neural network universal estimating) but according to the literature, using network will have complicated results. Since it is difficult to understand the linear and nonlinear data pattern in reality, this idea will come to mind that the combination of linear and nonlinear models could increase the accuracy of forecasting. So in this research the linear part will be estimated by ARIMA and then the non-linear residuals will be modeled by neural network and finally the predicted result will be added to ARIMA in order to forecast the low, high and close price of gold .comparing the accuracy of the hybrid model to ARIMA and neural network by pair compared, Diebold-Mariano and Harvey-Newbold –Leybourn test and two criteria (MSE and MAE) showed that the hybrid model presented better performance.