Distance-based Analysis of Ordinal Data and Ordinal Time Series

The dissimilarity of ordinal categories can be expressed with a distance measure. By considering expected distances of ordinal random variables, well-interpretable measures of location, dispersion or symmetry of ordinal random variables are defined, and also measures of serial dependence for ordinal processes. 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. Two real applications about the economic situation in Germany and the credit rating of European countries are presented.