Using the Gamma Memory Neural Network for Bankruptcy Prediction: a Preliminary Study

Many static neural networks have been studied extensively in financial classification problems. However, dynamic time series predictive classification using neural networks with memory, such as the Gamma Memory neural network (GMNN), may prove more accurate. In this study we compare the predictive accuracy of the GMNN to the Multilayer Perceptron neural network and the statistical approaches of Logistic Regression and Multiple Discriminant Analysis (MDA). Preliminary analysis of the GMNN versus other models gives mixed results. INTRODUCTION AND LITERATURE REVIEW The purpose of this research is to investigate if a time series classification method is able to predict potential bankruptcies more accurately than the static classification methods used since Altman’s original Z-score model. We test a neural network time series classification model (Gamma memory neural network) and contrast the decision accuracy with several prominent static classification methods. To our knowledge, there is no published research on the application of time series models to bankruptcy prediction. Bankruptcy prediction has been an area of interest for many decades. Altman (1968) studied bankruptcy prediction in his seminal work on MDA using financial ratios. Traditional methods of financial decision support include consumer credit scorecards (Brill, 1998; Henley, 1995; Mester, 1997; Reichert et al., 1983; Rosenberg and Gleit, 1994) and discriminant models for assessing corporate financial health (Altman et al., 1994; Reichert et al., 1983). Both are essentially multivariate linear models that output a probability that the client will repay debt as agreed. Neural networks have now come to the forefront as the preferred method for bankruptcy prediction (Kumar and Ravi, 2007). Many neural network architectures have been studied, including: the MLP neural network, the probabilistic neural network (PNN), the auto-associative neural network (AANN), self-roganizing maps (SOM), learning vector quantization (LVQ) and cascade correlation (Cascor). Many of the studies involving these neural networks continue to compare them with statistical techniques such as factor analysis, Logit, and various forms of discriminant analysis. In many of the cases the neural networks are reported to provide more accurate bankruptcy prediction capability than the parametric statistical approaches. However, the results are also often mixed. Tam and Kiang (1992), in an early treatment of neural networks in bankruptcy research, compared a variety of models. They studied MDA, Logit, K-nearest neighbor (KNN), a decision tree classification algorithm (ID3), a single-layer neural network, and a multi-layer neural network. The neural networks used were standard back-propagation (BPNN). The multi-layer network was the best for predicting bankruptcy using financial ratios one year ahead of bankruptcy. For two years ahead of bankruptcy, Logit was the best in the same studies. Salchenberger, et al. (1992), when considering the bankruptcies of thrifts, found the BPNN significantly outperformed Logit. In a comparison of the BPNN with MDA, Coats and Fant (1993) found the BPNN to be generally better, although it had a wider variance in the classification result depending on the horizon used. Altman et al. (1994) considered 1000 Italian firms in a bankruptcy study that compared a BPNN and MDA. For a one-year-ahead prediction, MDA appeared to perform slightly better than the BPNN. Boritz and Kennedy (1995) compared a number of techniques, including different BPNN training procedures, Logit, and MDA. The results of the comparisons were inconclusive. The BPNN has shown in many studies effectiveness in predicting bankruptcy that is mixed to good when compared to classical MDA and other approaches. Consequently, new hybrid techniques and genetic algorithms have recently begun to receive attention. Lee et al. (1996) tested combinations of the models such as MDA, ID3, self-organizing maps, and a BPNN. They studied bankruptcy prediction in Korean firms and reported that the self-organizing feature map assisted neural network performed best. Back et al. (1996) used genetic algorithms for input selection to a BPNN. The data in the study covered one to three years prior to bankruptcy. The BPNN was significantly better than MDA and Logit. Zhang et al. (1999) used a five-fold crossvalidation scheme on a group manufacturing firms, comparing a BPNN and Logit for bankruptcy prediction. The BPNN significantly outperformed Logit. McKee and Greenstein (2000) developed an approach based on decision trees. They applied it to a sample of US firms for financial health data one year ahead of bankruptcy. Their method gave better results than MDA and BPNN for Type II error, but worse results for Type I error. Atiya (2001) developed novel indicators extracted from the equity markets for a neural network system. They showed that the use of these indicators, in addition to traditional financial ratio indicators, gave a significant improvement in the bankruptcy prediction accuracy for the neural network. Forecasts were based on financial information three years in advance of bankruptcy. Pendharkar (2005) studied a threshold-varying artificial neural network (TV-ANN) for solving the bankruptcy prediction problem. Using a set of simulated and real-world data sets, the TV-ANN performed well when compared to the BPNN and the MDA. The performance comparisons of TV-ANN with a genetic algorithm-based ANN and a classification tree approach gave mixed results. In a study by Lee, et al. (2005), supervised and unsupervised neural networks were compared using their representative types. The BPNN and the Kohonen self-organizing feature map, selected as the representative type for supervised and unsupervised neural networks, respectively, were compared for bankruptcy prediction accuracy. MDA and Logit were also performed to provide performance benchmarks. The findings suggest that the BPNN is a better choice when a target vector is available. Lacking in all of these studies is an analysis of financial performance over time in making bankruptcy prediction. There is a reliance on information that is used to train the neural networks with data from one point in time – typically one or two years prior to bankruptcy. A time series approach would be desirable and could improve the accuracy of prediction. It has been shown in at least one application that the standard MLP, which is popular in bankruptcy prediction (Lee et al., 2005), underperforms neural networks that are designed to manage temporal effects. One such neural network is the GMNN. In a recent study of wastewater process control, which is characterized by nonlinear time varying dynamics, the Time Delay Neural Network -a less sophisticated version of the more general GMNN -was found to be superior to MLP in accuracy of prediction (Zhu et al., 1998). There is, therefore, reason to suspect that the GMNN will provide a better prediction of bankruptcy then the MLP in a dynamic time series application.