Modified nonlinear neural network forecasting models on Malaysian sand costs indices

Artificial Neural Networks (ANNs) have been adapted actively in the time series-prediction arena, but the presence of outliers that usually occur in the time series data may pollute the network training data. This is due to its ability to automatically learn any pattern without prior assumptions as well as loss of generality. In theory, the most common algorithm for training the network is the backpropagation (BP) algorithm which leans on the minimization of the ordinary least squares (OLS) estimator or more specifically, the mean squared error (MSE). Nonetheless, this algorithm is not entirely robust when the outliers are present, and it may lead to false prediction of future values. Therefore, in this current study, we present a new algorithm which manipulates the particle swarm optimization on the least median of squares (PSO-LMedS) estimator for artificial neural network nonlinear autoregressive moving average (ANN-NARMA) model to cater for the outlying issue in time series data. Additionally, the performance of the consolidated model with comparison with the other robust ANN-NARMA models using M-estimators, Iterative LMedS and Particle Swarm Optimization on LMedS with respect to mean squared error (MSE), mean absolute deviation (MAD), root mean squared error (RMSE), mean absolute percentage error (MAPE) and R-squared values are also highlighted in this paper. Meanwhile, the real-industrial monthly data of Malaysian Sand price index from January 1980 to December 2012 (base year 1980=100) were used. It was found that the robustified ANN-NARMA model using Least Median Square with Particle Swarm Optimization produced the best result with R-squared values equal to 100 in all training, testing and validation sets. It is expected that the findings would assist the respected authorities involve in PFI construction projects to overcome cost overruns.