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...has usually been considered to tackle this classification task. The objective of this paper is twofold. On the one hand, we apply the Adaboost.M1 algorithm to improve the accuracy of classification tree in a multiclass corporate failure prediction problem using a set of European firms. On the other, we introduce novel discerning measures to rank independent variables in a generic classification task.
Keywords Corporate failure prediction * Ensemble classifiers * Adaboost.M1
JEL C10 * G30 * M00
Introduction
As in any classification task, initially a set of n observations is given and noted as [T.sub.n] = {([X.sub.1],[Y.sub.1]), ([X.sub.2],[Y.sub.2]),..,([X.sub.n],[Y.sub.n])}, where each [X.sub.i] is a p-dimensional vector whose components are the values of the ith observation in each of the p features, that is to say i= {[X.sub.i1],[X.sub.i2],..., [X.sub.ip]} and Y is the observation class label and takes values in {1, 2,..., k}. On the basis of the training set, a classifier is constructed, in general, as a function of the p features, C([X.sub.i])=f([X.sub.i]). This function is used to predict the i class while minimizing the prediction error.
In a classification problem, a committee of classifiers can be used to increase the prediction accuracy, that is to say, it aggregates the predictions of several classifiers. Aggregation, combination and ensemble are synonymous in the literature of this field (Kuncheva 2004; Valentini and Masulli 2002). The classifier built combining some classifiers is called an ensemble of classifiers. There are several alternatives here, the first one being to build different classifiers from the data set and then combine them by simple vote or linear functions. Another possibility, perhaps more sophisticated, consists in applying the same classification method in modified versions of the learning set. Some of these techniques are quite new and have been studied quite closely in the last few years, among which, bagging and boosting methods deserve a special mention (Freund and Schapire 1996, 1997; Breiman 1998).
Although in corporate failure prediction literature only a binary classification problem is usually considered to differentiate failed from healthy firms, it makes sense to think that there are more than one type of failure. For instance, in the Spanish case only bankruptcy and temporary receivership firms are traditionally considered as failed firms, but it seems that there are other types of failure. In this study acquired and dissolved firms are also included as failed firms. We analyze whether these firms have a different financial behaviour with respect to healthy firms. With this aim, the application works with a three classes problem (healthy, failed1, and failed2), where failed1 includes acquired and dissolved firms, and failed2 includes bankruptcy and temporary receivership. The question here is if discriminating between two different states of failure is possible.
In this research, a new algorithm is proposed for predicting corporate failure. To show its utility, we apply this method over a sample of Spanish companies. In order to guarantee that our results have a general character and can be extrapolated to both European countries and the United States, we use financial ratios that have been found significant in predicting business failure in previous studies, such as Frydman et al. (1985).
Furthermore, a novel measure for the importance of variables is proposed to facilitate model interpretation. This measure takes into account how many times each variable is actually used throughout the individual trees. On the basis of this measure, the variables can be ranked in terms of importance.
Within the empirical application the following factors should be taken into account:
* Not only bankruptcy and temporary receivership firms as is usual in corporate failure prediction literature, but also acquired and dissolved firms are considered.
* Not only the usual financial ratios are included as predictors, but also qualitative variables, such as the firm size, activity, and legal structure.
* The Adaboost.M1 algorithm is applied to the corporate prediction, analysing the extent to which this methodology is suitable for the subject.
The paper is organized as follows. First, we present the boosting method included in the study. We then discuss how it works in practice, together with the Adaboost.M1 algorithm used. The following section introduces the failure prediction problem and the data used in the analysis. The classification results are then presented, with a comparison of the well-known classification tree model with the novel Adaboost.M1 classifier. The empirical analysis is followed...
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