An out-of-sample framework for TOPSIS-based classifiers with application in bankruptcy prediction

Highlights

• TOPSIS classifiers lack a proper framework for out-of-sample evaluation.

• An in-sample-out-of-sample framework for TOPSIS classifiers is proposed.

• Its performance is tested on a UK dataset of bankrupt and non-bankrupt firms.

• Results show an outstanding predictive performance in-sample and out-of-sample.

• Out-of-sample framework makes TOPSIS classifiers real contenders for practitioners.

Abstract

Since the publication of the seminal paper by Hwang and Yoon (1981) proposing Technique for Order Performance by the Similarity to Ideal Solution (TOPSIS), a substantial number of papers used this technique in a variety of applications requiring a ranking of alternatives. Very few papers use TOPSIS as a classifier (e.g. Wu and Olson, 2006; Abd-El Fattah et al., 2013) and report a good performance as in-sample classifiers. However, in practice, its use in predicting discrete variables such as risk class belonging is limited by the lack of an out-of-sample evaluation framework. In this paper, we fill this gap by proposing an integrated in-sample and out-of-sample framework for TOPSIS classifiers and test its performance on a UK dataset of bankrupt and non-bankrupt firms listed on the London Stock Exchange (LSE) during 2010–2014. Empirical results show an outstanding predictive performance both in-sample and out-of-sample and thus opens a new avenue for research and applications in risk modelling and analysis using TOPSIS as a non-parametric classifier and makes it a real contender in industry applications in banking and investment. In addition, the proposed framework is robust to a variety of implementation decisions.

Introduction

Multi-criteria decision analysis (MCDA) methodologies are widely used for addressing a variety of problems; namely, selection problems, ranking problems, sorting problems, classification problems, clustering problems, and description problems, where selection problems are concerned with identifying the best alternative or a subset of best alternatives; ranking problems are concerned with constructing a rank ordering of alternatives from best to worst; sorting problems are concerned with classifying alternatives into pre-defined and ordered homogenous groups or classes; classification problems are concerned with classifying alternatives into pre-defined and unordered homogenous classes; clustering problems are concerned with classifying alternatives into not pre-defined and not ordered homogenous classes; and description problems are concerned with identifying major distinguishing features of alternatives and perform their description based on these features. In this paper, we are focusing on the solution of classification problems, or equivalently predicting class belonging. To be more specific, we are concerned with the implementation of classifiers and their performance evaluation both in-sample and out-of-sample.

One popular MCDA methodology is Technique for Order Performance by the Similarity to Ideal Solution (TOPSIS) proposed by Hwang and Yoon (1981) and used in many application areas – see Behzadian et al. (2012) for a review including a sample of application areas. This methodology was originally designed for solving ranking problems. In fact, TOPSIS provides a ranking of alternatives based on similarity scores, where the similarity score of each alternative is a function of the distances between the alternative and a couple of benchmarks commonly referred to as the positive and the negative ideal solutions. Later on, TOPSIS has been adapted for solving classification problems. However, to the best of our knowledge, TOPSIS classifiers and their performance evaluation has so far been restricted to in-sample analyses only (e.g., Tansel and Yurdakul, 2010, Abd-El Fattah et al., 2013). In sum, an out-of-sample framework for TOPSIS as a classifier is lacking. The aim of this paper is to fill this gap by proposing a new integrated framework for implementing a full classification analysis; namely, in-sample classification and out-of-sample classification. The proposed framework is intended to make TOPSIS classifiers real contenders in practice and to increase confidence in their use in a variety of critical application areas such as the prediction of risk class belonging (e.g., bankruptcy prediction, distress prediction, fraud detection, credit scoring).

The remainder of this paper unfolds as follows. In Section 2, we provide a detailed description of the proposed integrated in-sample and out-of-sample framework for TOPSIS classifiers and discuss implementation decisions. In Section 3, we empirically test the performance of the proposed framework in bankruptcy prediction of companies listed on the London Stock Exchange (LSE) and report on our findings. Finally, Section 4 concludes the paper.