Analysing the Returns-Earnings Relationship: Dempster-Shafer Theory and Evolutionary Computation Based Analyses Using the Classification and Ranking Belief Simplex

Analysing the Returns-Earnings Relationship: Dempster-Shafer Theory and Evolutionary Computation Based Analyses Using the Classification and Ranking Belief Simplex

Malcolm J. Beynon (Cardiff University, UK,) and Mark Clatworthy (Cardiff University, UK,)
DOI: 10.4018/978-1-4666-2086-5.ch007
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Abstract

This chapter considers the problem of understanding the relationship between company stock returns and earnings components, namely accruals and cash flows. The problem is of interest, because earnings are a key output of the accounting process, and investors have been shown to depend heavily on earnings in their valuation models. This chapter offers an elucidation on the application of a nascent data analysis technique, the Classification and Ranking Belief Simplex (CaRBS) and a recent development of it, called RCaRBS, in the returns-earnings relationship problem previously described. The approach underpinning the CaRBS technique is closely associated with uncertain reasoning, with methodological rudiments based on the Dempster-Shafer theory of evidence. With the analysis approach formed as a constrained optimisation problem, details on the employment of the evolutionary computation based technique trigonometric differential evolution are also presented. Alongside the presentation of results, in terms of model fit and variable contribution, based on a CaRBS classification-type analysis, a secondary analysis is performed using a development RCaRBS, which is able to perform multivariate regression-type analysis. Comparisons are made between the results from the two different types of analysis, as well as briefly with more traditional forms of analysis, namely binary logistic regression and multivariate linear regression. Where appropriate, numerical details in the construction of results from both CaRBS and RCaRBS are presented, as well emphasis on the graphical elucidation of findings.
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Background

The Classification and Ranking Belief Simplex (CaRBS) technique was originally devised as a tool to undertake the binary classification and ranking of objects in the presence of ignorance (see Beynon, 2005a). The background discussed here surrounds the related technical issues, namely an exposition of the CaRBS technique and the development of it, called RCaRBS, which enables regression-type analyses to be performed (see Beynon et al., 2010), and the power house methodology behind the necessary configuration optimisation, namely the evolutionary computation approach TDE.

The methodology underpinning the CaRBS technique is Dempster-Shafer theory (DST), introduced in Dempster (1967) and Shafer (1976), and generally acknowledged to be a mathematical approach associated with uncertainty modelling (Roesmer, 2000). Fundamentally, DST is based on the idea of obtaining degrees of belief for one question (the equivalent of a dependent variable), from subjective probabilities describing the evidence from others (the equivalent of independent variables), and that the concordance of pieces of evidence reinforce each other. This uncertain reasoning methodology, it has been argued, is a generalization of the well-known Bayesian probability calculus (Shafer and Srivastava, 1990; Schubert, 1994).

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