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This paper introduces a new framework to quantify distance between finitesets with uncertainty present, where probability distributions determine thelocations of individual elements. Combining this with a Bayesian change pointdetection algorithm, we produce a new measure of similarity between time serieswith respect to their structural breaks. First, we demonstrate the algorithm'seffectiveness on a collection of piecewise autoregressive processes. Next, weapply this to financial data to study the erratic behavior profiles of 19countries and 11 sectors over the past 20 years. Our measure providesquantitative evidence that there is greater collective similarity amongsectors' erratic behavior profiles than those of countries, which we observeupon individual inspection of these time series. Our measure could be used as anew framework or complementary tool for investors seeking to make assetallocation decisions for financial portfolios.

A new measure between sets of probability distributions with applications to erratic financial behavior