Applications of random-matrix theory and nonparametric change-point analysis to three notable systemic crises

David Melkuev; Danqiao Guo; Tony S. Wirjanto; David Melkuev; Danqiao Guo; Tony S. Wirjanto

doi:10.3934/QFE.2018.2.413

Quantitative Finance and Economics

2018, Volume 2, Issue 2: 413-467. doi: 10.3934/QFE.2018.2.413

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Applications of random-matrix theory and nonparametric change-point analysis to three notable systemic crises

1.
Canada Pension Plan Investment BoardOne Queen Street East, Suite 2500, Toronto, ON M5C 2W5, Canada
2.
Department of Statistics & Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
3.
School of Accounting & Finance, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada

Received: 28 November 2017 Accepted: 22 April 2018 Published: 11 June 2018
JEL Codes: C1, F4, G1

This paper studies association between changes in absorption ratio and aggregate market returns in three systemic crises across a broad class of assets. Time series of normalized eigenvalue estimates reveal that crises are characterized by a general breakdown of correlation structure. The structure of return correlations is nonlinear and nonstationary across di erent asset groups. So we introduce a nonparametric technique to monitor divergence in distributions underlying successive observations of normalized dominant eigenvalue of the returns. Periods of high divergence imply a change in the correlation structure of asset returns. They are found to either precede or coincide with systemic shocks. An additional parametric analysis is provided as an informal check on the results obtained in the paper.
- global financial crisis,
- Eurozone sovereign debt crisis,
- Asian financial crisis,
- equities,
- bonds,
- CDS,
- contract,
- principal component analysis,
- random matrix theory,
- nonparametric changepoint analysis
Citation: David Melkuev, Danqiao Guo, Tony S. Wirjanto. Applications of random-matrix theory and nonparametric change-point analysis to three notable systemic crises[J]. Quantitative Finance and Economics, 2018, 2(2): 413-467. doi: 10.3934/QFE.2018.2.413

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Abstract

This paper studies association between changes in absorption ratio and aggregate market returns in three systemic crises across a broad class of assets. Time series of normalized eigenvalue estimates reveal that crises are characterized by a general breakdown of correlation structure. The structure of return correlations is nonlinear and nonstationary across di erent asset groups. So we introduce a nonparametric technique to monitor divergence in distributions underlying successive observations of normalized dominant eigenvalue of the returns. Periods of high divergence imply a change in the correlation structure of asset returns. They are found to either precede or coincide with systemic shocks. An additional parametric analysis is provided as an informal check on the results obtained in the paper.

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