Consistent Estimation of Multiple Breakpoints in Dependence Measures

Abstract

This article proposes different methods to consistently detect multiple breaks in copula-based dependence measures. Starting with the classical binary segmentation, also the more recent wild binary segmentation (WBS) is considered. For binary segmentation, consistency of the estimators for the location of the breakpoints as well as the number of breaks is proved, taking filtering effects from AR-GARCH models explicitly into account. Monte Carlo simulations based on a factor copula as well as on a Clayton copula model illustrate the strengths and limitations of the procedures. A real data application on recent Euro Stoxx 50 data reveals some interpretable breaks in the dependence structure.

KEYWORDS:

• AR-GARCH residuals
• Clayton copula
• Factor copula
• (Wild) binary segmentation

Disclosure Statement

The authors report there are no competing interests to declare.

Notes

1 The following can be readily extended to ${\mathcal{l}}^0>2$: Similar to the case with ${\mathcal{l}}^0=2$ breakpoints, one has to distinguish between ${\mathcal{l}}^0+1+{\mathcal{l}}^0({\mathcal{l}}^0+1)/2$ cases; that is, ${\mathcal{l}}^0+1$ cases with no breaks located within $[a,z]\text{ and }{\mathcal{l}}^0({\mathcal{l}}^0+1)/2$ cases with at least one break located within $[a,z]$.

Additional information

Funding

Financial support by Deutsche Forschungsgemeinschaft (DFG grant ‘Strukturbrüche und Zeitvariation in hochdimensionalen Abhängigkeitsstrukturen’) is gratefully acknowledged. Moreover, we are grateful to helpful comments from the Editor Atsushi Inoue, an associate editor and two referees. The computations were implemented in Matlab, parallelized and performed using CHEOPS, the DFG-funded (Funding number: INST 216/512/1FUGG) High Performance Computing (HPC) system of the Regional Computing Center at the University of Cologne (RRZK).