Compositional data are contemporarily defined as positive vectors, the ratios among whose elements are of interest to the researcher. Financial statement analysis by means of accounting ratios fulfils this definition to the letter. Compositional data analysis solves the major problems in statistical analysis of standard financial ratios at industry level, such as skewness, non-normality, non-linearity and dependence of the results on the choice of which accounting figure goes to the numerator and to the denominator of the ratio. In spite of this, compositional applications to financial statement analysis are still rare. In this article, we present some transformations within compositional data analysis that are particularly useful for financial statement analysis. We show how to compute industry or sub-industry means of standard financial ratios from a compositional perspective. We show how to visualise firms in an industry with a compositional biplot, to classify them with compositional cluster analysis and to relate financial and non-financial indicators with compositional regression models. We show an application to the accounting statements of Spanish wineries using DuPont analysis, and a step-by-step tutorial to the compositional freeware CoDaPack.

翻译：成分数据目前被定义为正向量，其各元素之间的比值是研究者关注的重点。通过会计比率进行的财务报表分析完全符合这一定义。成分数据分析解决了行业层面标准财务比率统计分析中的主要问题，如偏态、非正态性、非线性以及结果对比率分子和分母中会计数字选择依赖性的问题。尽管如此，成分数据分析在财务报表分析中的应用仍然少见。在本文中，我们介绍了成分数据分析中特别适用于财务报表分析的一些变换。我们展示了如何从成分视角计算行业或子行业标准财务比率的均值。我们展示了如何通过成分双标图可视化行业内的企业，通过成分聚类分析对其进行分类，以及通过成分回归模型关联财务与非财务指标。我们以杜邦分析为例，对西班牙酒庄的会计报表进行了应用分析，并提供了成分分析免费软件CoDaPack的逐步教程。