Multiple break detection in the correlation structure of random variables

TL;DR

This paper introduces a binary segmentation method to detect multiple change points in the correlation structure of random variables, which is crucial for financial analysis during crises, and proves its asymptotic correctness with simulations and empirical data.

Contribution

A novel binary segmentation algorithm for identifying multiple correlation change points, with proven asymptotic consistency and demonstrated effectiveness through simulations and real data.

Findings

Algorithm asymptotically detects correct number of change points

Consistent estimation of change point locations

Effective in empirical financial data analysis

Abstract

Correlations between random variables play an important role in applications, e.g.\ in financial analysis. More precisely, accurate estimates of the correlation between financial returns are crucial in portfolio management. In particular, in periods of financial crisis, extreme movements in asset prices are found to be more highly correlated than small movements. It is precisely under these conditions that investors are extremely concerned about changes on correlations. A binary segmentation procedure to detect the number and position of multiple change points in the correlation structure of random variables is proposed. The procedure assumes that expectations and variances are constant and that there are sudden shifts in the correlations. It is shown analytically that the proposed algorithm asymptotically gives the correct number of change points and the change points are consistently estimated. It is also shown by simulation studies and by an empirical application that the algorithm yields reasonable results.