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

TL;DR

This paper presents a novel measure for quantifying similarity between sets of probability distributions, with applications in detecting structural breaks in time series and analyzing erratic financial behaviors across countries and sectors.

Contribution

It introduces a new distance measure between probabilistic sets combined with a Bayesian change point detection algorithm for analyzing structural breaks in time series.

Findings

Effective detection of structural breaks in autoregressive processes

Greater similarity in erratic behavior among sectors than countries

Potential use as a tool for financial asset allocation

Abstract

This paper introduces a new framework to quantify distance between finite sets with uncertainty present, where probability distributions determine the locations of individual elements. Combining this with a Bayesian change point detection algorithm, we produce a new measure of similarity between time series with respect to their structural breaks. First, we demonstrate the algorithm's effectiveness on a collection of piecewise autoregressive processes. Next, we apply this to financial data to study the erratic behavior profiles of 19 countries and 11 sectors over the past 20 years. Our measure provides quantitative evidence that there is greater collective similarity among sectors' erratic behavior profiles than those of countries, which we observe upon individual inspection of these time series. Our measure could be used as a new framework or complementary tool for investors seeking to make asset allocation decisions for financial portfolios.