Hybrid computational intelligence systems based on statistical and neural networks methods for time series forecasting: the case of gold price

Abstract

In this research, two hybrid systems are proposed whose components are the Autoregressive Integrated Moving Average (ARIMA) model, and two types of Artificial Neural Networks (ANN) models. Since there are many types of ANN, this study focused on the Multilayer Perceptron (MLP) and Elman Recurrent Neural Networks (ERNN or Elman). Toward improving the performance of the MLP, Genetic Algorithm (GA) was also employed to optimise the weights and the neurons in the hidden layer of the MLP. Thus, three different ANN models were investigated. These three ANN in addition to ARIMA were used for modelling three time series. These series were the average yearly gold price, the average monthly gold price, and the daily gold price (London PM Fix) where all the values were in US dollars. This study focused on investigating the possibility of finding an accurate model to forecast the gold prices and, more specifically, to investigate whether a hybrid system will improve the forecasting results of three gold price series: yearly, monthly and daily. To achieve these goals, two hybrid systems were developed to capture both linear and nonlinear components in the gold price series. The first hybrid system is a combination of ARIMA and MLP and the second combines ARIMA with Elman. The building blocks of the two proposed hybrid approaches contained three steps: in the first step ARIMA model is used to model the gold price series; second, two types of neural networks (MLP and Elman) were built to model the residuals from the ARIMA model. In addition to this and in order to improve the forecast iii accuracy, the number of neurons in the hidden layer and the weights of MLP were optimised by GA (GA-MLP). The optimisation result was unsatisfactory, hence GA-MLP model were excluded. Finally, the forecast from the ARIMA and the two ANN models, Elman and MLP were combined to forms the hybrid systems aimed in this study. The performance of each single model, ARIMA, MLP and Elman along with hybrid models were compared. The results obtained in this study showed that compared to the ARIMA and ANN approaches, the proposed hybrid models performed much better in the monthly and yearly predictions but yielded the same results in the daily forecasts.