Cross Entropy Error Function in Neural Networks: Forecasting Gasoline Demand

This paper applies artificial neural networks to forecast gasoline consumption. The ANN is implemented using the cross entropy error function in the training stage. The cross entropy function is proven to accelerate the backpropagation algorithm and to provide good overall network performance with relatively short stagnation periods. To forecast gasoline consumption (GC), the ANN uses previous GC data and its determinants in a training data set. The determinants of gasoline consumption employed in this study are the price (P) and car registration (CR). Two ANNs models are presented. The first model is a univariate model based on past GC values. The second model is a trivariate model based on GC, price and car registration time series. Forecasting performance measures such as mean square errors (MSE) and mean absolute deviations (MAD) are presented for both models. Introduction The estimation of future demand for gasoline consumption is central to the planning of transportation systems. Such planning is improved through investigating a whole range of forecasting techniques. In addition, in order to guarantee a regular supply of gasoline, vital to the economic cycle of a country, it is necessary to keep a reserve. Depending on how fast this form of energy can become available, this reserve bears the name of spinning reserve or of cold reserve. Overestimating the future gasoline consumption results in unused spinning reserve and underestimating the future consumption is equally detrimental. Thus, using accurate forecasting techniques becomes essential (Darbellay and Slama, 2000). For many years, researchers have sought to understand consumer response to changes in the price of gasoline so as to design effective energy and environmental policy (Puller and Greening, 1999). The majority of studies have estimated the price elasticity of gasoline demand using aggregatelevel data. This large number of studies has produced greatly varying estimates of the price elasticity depending on the specification and the data used. Also, estimating gasoline demand using household level data rather than aggregate data provides estimates that reflect more closely how individual consumers respond to changes in gasoline prices or household income (Kayser, 2000). Recent research activities in artificial neural networks (ANNs) have shown that ANNs have powerful pattern classification and pattern recognition capabilities. Thus, one major application area of ANNs is forecasting (Sharda, 2000). Also, ANNs are well suited for problems whose solutions require knowledge that is difficult to specify but for which there are enough data or observations (Zhang, Patuwo and Hu, 1998). Research efforts on ANNs and other statistical means used for forecasting are considerable (Nasr, Badr and Younes, 2001; Nasr, Badr and Dibeh, 2000; Saab, Badr and Nasr, 2000). In this paper, two neural network models suited to forecast monthly gasoline consumption in Lebanon are built. The first model is a univariate and fully connected model based on past GC values. The second model is a trivariate not fully connected model based on past GC values, gasoline price (P) and car registration (CR). Historically, a large number of studies offer a direct relationship between energy consumption and the price of energy. This paper presents no exception in this regard, but also ties gasoline consumption to car registration, since a change in the volume of operating cars would also affect the consumption of gasoline. The data used in this study is extracted from a governmental report (Statistical Administration, 1993-1999). The predictions are made using feed-forward neural networks since they are able to learn nonlinear mappings between inputs and outputs. Also, we propose to replace the common mean square error (MSE) by the cross-entropy error function in which the error signal associated with the output layer is directly proportional to the difference between the desired and actual output values. The cross entropy function is proven to accelerate the backpropagation algorithm and to provide good overall network performance with relatively short stagnation periods. FLAIRS 2002 381 From: FLAIRS-02 Proceedings. Copyright © 2002, AAAI (www.aaai.org). All rights reserved.