How Good Are Neural Networks for Causal Forecasting

A new artificial intelligence tool, the neural network, offers an alternative to multiple regression for performing causal forecasts. This study shows that under ideal conditions there is little difference in predictability between models based on regression and those based on a neural network. But under less than ideal conditions (when there is an outlier in the data, when two independent variables are highly correlated, or when the model is mis-specified), neural networks do a better job. NEURAL NETWORKS IN PATTERN RECOGNITION Neural networks utilize a system of highly interconnected nodes, or neurons, to emulate (in a simplistic way) the operation of the brain. As such, they are an attractive choice for pattern recognition problems since the brain is unsurpassed by any current computer-based technique in its ability to recognize patterns. A typical pattern recognition problem, in which a neural network has outperformed computer-based techniques, involves recognizing sonar signal reflections from mines and rocks. This application used input data in the form of coded numbers extracted from sonar reflection patterns to predict whether those patterns resulted from mines or rocks. In causal forecasting, input data representing the values of independent variables will be used by a neural network to predict the value of a dependent variable. To accomplish this, the neural network will be trained with historical data to recognize relevant patterns in the independent variables. Neural networks can be characterized by their architecture, or arrangement of nodes and arcs. A typical architecture used in causal forecasting has the nodes arranged in three layers: an input layer at the bottom, a hidden layer in the middle, and an output layer at the top. The input layer contains one node for each independent variable, which are connected by arcs to the nodes in the hidden layer. There can be any number of nodes in this layer, but it typically does not exceed twice the number of input nodes. Nodes in the hidden layer are connected by arcs to the nodes in the output layer, which contains one node for each dependent variable. In this study, only one dependent variable was considered, so the output layer contained a single node. Typically, each node is connected to every node in the next higher layer by an arc, which has an associated weight. For each observation in the historical data set, the forecaster must provide the values of the independent variables as inputs. The network then computes the activation levels of the nodes in the hidden layer and the output layer as functions of the arc weights. The activation level of the output node is used to predict the value of the dependent variable. Neural networks can be easily designed and tested using several commercially available software packages for the personal computer. One such package from NeuralWare, Inc., is called "BrainMaker." This study utilized software designed by the author. As in regression, the historical data are used to determine the parameter values that produce the smallest mean squared error (MSE). In the case of the neural network, the parameters are the arc weights. Determining the proper arc weights is done in the process of neural network training. Training is accomplished through a sequence of iterations that adjust the arc weights until a satisfactory solution is achieved for the historical data set. The most popular training algorithm is called back propagation. REGRESSION VS. NEURAL NETWORKS Both regression and neural networks seek to minimize the MSE between actual and desired responses. But the modeling responsibilities of the forecaster differ for the two approaches. The regression approach requires that a functional form, which characterizes the relationship between the variables, be specified. A neural network does not require this level of modeling, but there are still significant decisions to be made by the forecaster. …