Principal Component Analysis to Reduce Forecasting Error of Industrial Energy Consumption in Models Based on Neural Networks

Abstract

Industrial energy consumption depends on social and economic variables, and the way in which variables are selected is an important issue in causal forecasting. In this paper, we have developed a method to select the input variables for the monthly forecasting of energy consumption by artificial neural networks. The method consists of applying principal component analysis to reduce the dimensionality of data. The forecasts obtained by applying the principal component analysis were combined by a neural network and compared to the ones obtained by selecting variables using a correlation analysis. An important contribution of this work is the evidence that principal component analysis reduces the number of variables in the input set and, consequently, the error rate of neural networks in energy forecasting. The Mean Absolute Percentage Error (MAPE) and Theil’s U statistic were used to provide evidence of the predictive capability of the proposed method. The neural network with variables selected via the first principal component analysis obtained out of sample errors of that were approximately 15.4% lower than the neural nets with input variables selected by correlation analysis. In addition, the performance of the neural net, the input of which was selected in the second principal component, has demonstrated a MAPE that was 10.65% lower than the neural net fed with variables selected using a correlation analysis. Completing the analysis, the combination of forecasts exhibited errors that were approximately 0.93% lower than the error obtained by selecting variables using a correlation analysis. The neural net that was fed with variables selected in the third principal component did not reach errors lower than the naive method. However, the nets results were relevant to the combination of forecasts.