Distance-Based Analysis of Ordinal Data and Ordinal Time Series

The dissimilarity of ordinal categories can be expressed with a distance measure. A unified approach relying on expected distances is proposed to obtain well-interpretable measures of location, dispersion, or symmetry of random variables, as well as measures of serial dependence within a given process. For special types of distance, these analytic tools lead to known approaches for ordinal or real-valued random variables. We also analyze the sample counterparts of the proposed measures and derive asymptotic results for practically important cases in ordinal data and time series analysis. Two real applications about the economic situation in Germany and the credit rating of European countries are presented. Supplementary materials for this article are available online.