Skip to main content
SpringerLink
Log in

Testing for relevant dependence change in financial data: a CUSUM copula approach

  • Published:
Empirical Economics Aims and scope Submit manuscript

Abstract

We propose a new nonparametric test for detecting relevant breaks in copula functions. We assume that the data is driven by two non-equal copulas \(C_1\) and \(C_2\). Under the null hypothesis, the copula difference within an appropriate norm is smaller than a certain positive adjustable threshold \(\varDelta \). Within the alternative hypothesis, the copula difference exceeds the fixed value \(\varDelta \). The test is based on a cumulative sum approach of the empirical copula with sequentially estimated marginals. We propose a bootstrap procedure to compute critical values. The Monte Carlo simulation indicates that the test results in a reasonable sized and powered testing procedure. A real data application of the DAX30 up to cross-sectional dimension \(N=30\) shows the test’s ability to detect relevant break points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. Due to the fact that this discussion is very technical, we shifted the details to Supplemental Appendix.

  2. For the very detailed derivation of the testing procedure, we refer to Supplemental Appendix.

  3. Note, \(\hat{s}\) is a superconsistent estimator of the changepoint fraction s with convergence rate T (cf. Dette and Wied 2016).

  4. As in Oh and Patton (2017) this refers to the skewed t-distribution by Hansen (1994).

  5. We adjusted the estimate for \(5\%\) of their outliers by setting these values equal to the expected value.

References

  • Aloui R, Aïssa MSB, Nguyen DK (2011) Global financial crisis, extreme interdependences, and contagion effects: the role of economic structure? J Bank Finance 35(1):130–141

    Article  Google Scholar 

  • Berkson J (1938) Some difficulties of interpretation encountered in the application of the chi-square test. J Am Stat Assoc 33:526–536

    Article  Google Scholar 

  • Brodsky B, Penikas H, Safaryan I et al (2009) Detection of structural breaks in copula models. Appl Econom 16(4):3–15

    Google Scholar 

  • Bücher A, Ruppert M (2013) Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique. J Multivar Anal 116:208–229

    Article  Google Scholar 

  • Bücher A, Kojadinovic I, Rohmer T, Segers J (2014) Detecting changes in cross-sectional dependence in multivariate time series. J Multivar Anal 132:111–128

    Article  Google Scholar 

  • Busetti F, Harvey A (2011) When is a copula constant? A test for changing relationships. J Financ Econom 9:106–131

    Article  Google Scholar 

  • Dehling H, Vogel D, Wendler M, Wied D (2017) Testing for changes in Kendall’s Tau. Econom Theory 33:1352–1386

    Article  Google Scholar 

  • Dette H, Gösmann J (2017) Relevant change points in high dimensional time series. Working paper. arXiv:1704.04614

  • Dette H, Wied D (2016) Detecting changes in time series models. J Roy Stat Soc B 78:371–394

    Article  Google Scholar 

  • Dette H, Wu W, Zhou Z (2018) Change point analysis of second order characteristics in non-stationary time series. Stat Sin (forthcoming)

  • Hansen EB (1994) Autoregressive density estimation. Int Econ Rev 35:705–730

    Article  Google Scholar 

  • Krämer W, van Kampen M (2011) A simple nonparametric test for structural change in joint tail probabilities. Econ Lett 110:245–247

    Article  Google Scholar 

  • Manner H, Stark F, Wied D (2019) Testing for structural breaks in factor copula models. J Econ 208:324–345

    Article  Google Scholar 

  • Oh D, Patton A (2017) Modelling dependence in high dimensions with factor copulas. J Bus Econ Stat 35:139–154

    Article  Google Scholar 

  • Wied D, Dehling H, van Kampen M, Vogel D (2013) A fluctuation test for constant spearmans’s rho with nuisance-free limit distribution. Comput Stat Data Anal 76:723–736

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cologne, Universitätsstr. 24, 50937, Cologne, Germany

    Tim Kutzker, Florian Stark & Dominik Wied

Authors
  1. Tim Kutzker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florian Stark
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dominik Wied
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Stark.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Research is supported by Deutsche Forschungsgemeinschaft MA 7225/1-1, AOBJ 628937 (DFG Grant “Strukturbrüche und Zeitvariation in hochdimensionalen Abhängigkeitsstrukturen”).

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 403 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kutzker, T., Stark, F. & Wied, D. Testing for relevant dependence change in financial data: a CUSUM copula approach. Empir Econ 60, 1875–1894 (2021). https://doi.org/10.1007/s00181-019-01811-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00181-019-01811-4

Keywords

JEL Classification

Search

Navigation