Advertisement

Metrika

, Volume 81, Issue 6, pp 653–687 | Cite as

A residual-based multivariate constant correlation test

  • Fang Duan
  • Dominik Wied
Article

Abstract

We propose a new multivariate constant correlation test based on residuals. This test takes into account the whole correlation matrix instead of the considering merely marginal correlations between bivariate data series. In financial markets, it is unrealistic to assume that the marginal variances are constant. This motivates us to develop a constant correlation test which allows for non-constant marginal variances in multivariate time series. However, when the assumption of constant marginal variances is relaxed, it can be shown that the residual effect leads to nonstandard limit distributions of the test statistics based on residual terms. The critical values of the test statistics are not directly available and we use a bootstrap approximation to obtain the corresponding critical values for the test. We also derive the limit distribution of the test statistics based on residuals under the null hypothesis. Monte Carlo simulations show that the test has appealing size and power properties in finite samples. We also apply our test to the stock returns in Euro Stoxx 50 and integrate the test into a binary segmentation algorithm to detect multiple break points.

Keywords

Structural breaks Hypothesis testing Correlation Residual effect 

JEL Classification

C12 C32 C58 

Notes

Acknowledgements

F. Duan gratefully acknowledges funding by Ruhr Graduate School in Economics (RGS Econ).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author (D. Wied) states that there is no conflict of interest concerning this paper.

Supplementary material

References

  1. Andrews D (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59(3):817–858MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aue A, Hörmann S, Horváth L, Reimherr M (2009) Break detection in the covariance structure of multivariate time series models. Ann Stat 37(6B):4046–4087MathSciNetCrossRefzbMATHGoogle Scholar
  3. Bai J, Ng S (2005) Tests for skewness, kurtosis, and normality for time series data. J Bus Econ Stat 23(1):49–60MathSciNetCrossRefGoogle Scholar
  4. Berens T, Weiß GN, Wied D (2015) Testing for structural breaks in correlations: does it improve value-at-risk forecasting? J Empir Finance 32(C):135–152CrossRefGoogle Scholar
  5. Brown RL, Durbin J, Evans JM (1975) Techniques for testing the constancy of regression relationships over time. J R Stat Soc Ser B (Methodol) 37(2):149–192MathSciNetzbMATHGoogle Scholar
  6. Carlstein E (1986) The use of subseries values for estimating the variance of a general statistic from a stationary sequence. Ann Stat 14(3):1171–1179MathSciNetCrossRefzbMATHGoogle Scholar
  7. Davidson J (1994) Stochastic Limit Theory, Advanced Texts in Econometrics. Oxford University Press, OxfordCrossRefGoogle Scholar
  8. Demetrescu M, Wied D (2018) Testing for constant correlaton of filtered series under structural change. Econ J, forthcoming.  https://doi.org/10.1111/ectj.12116
  9. Galeano P, Wied D (2014) Multiple break detection in the correlation structure of random variables. Comput Stat Data Anal 76(C):262–282MathSciNetCrossRefGoogle Scholar
  10. Galeano P, Wied D (2017) Dating multiple change points in the correlation matrix. TEST Off J Span Soc Stat Oper Res 26(2):331–352MathSciNetzbMATHGoogle Scholar
  11. Guillén MF (2015) The global economic and financial crisis: a timeline. Unpublished manuscriptGoogle Scholar
  12. Hall P, Horowitz J (1996) Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica 64(4):891–916MathSciNetCrossRefzbMATHGoogle Scholar
  13. Hansen L (1982) Large sample properties of generalized method of moments estimators. Econometrica 50(4):1029–54MathSciNetCrossRefzbMATHGoogle Scholar
  14. Inoue A, Shintani M (2006) Bootstrapping GMM estimators for time series. J Econom 133(2):531–555MathSciNetCrossRefzbMATHGoogle Scholar
  15. Kiefer J (1959) K-sample analogues of the Kolmogorov–Smirnov and Cramér–V. Mises tests. Ann Math Stat 30(2):420–447CrossRefzbMATHGoogle Scholar
  16. Lahiri SN (1999) Theoretical comparisons of block bootstrap methods. Ann Stat 27(1):386–404MathSciNetCrossRefzbMATHGoogle Scholar
  17. Lahiri SN (2003) Resampling Methods for Dependent Data, Springer Series in Statistics, 1st edn. Springer, New YorkCrossRefGoogle Scholar
  18. Pape K, Wied D, Galeano P (2016) Monitoring multivariate variance changes. J Empir Finance 39(PA):54–68CrossRefGoogle Scholar
  19. Ploberger W, Krämer W (1992) The CUSUM test with OLS residuals. Econometrica 60(2):271–285MathSciNetCrossRefzbMATHGoogle Scholar
  20. Politis DN, White H (2004) Automatic block-length selection for the dependent bootstrap. Econom Rev 23(1):53–70MathSciNetCrossRefzbMATHGoogle Scholar
  21. Wied D (2017) A nonparametric test for a constant correlation matrix. Econom Rev 36(10):1157–1172MathSciNetCrossRefGoogle Scholar
  22. Wied D, Arnold M, Bissantz N, Ziggel D (2012a) A new fluctuation test for constant variances with applications to finance. Metrika 75(8):1111–1127MathSciNetCrossRefzbMATHGoogle Scholar
  23. Wied D, Krämer W, Dehling H (2012b) Testing for a change in correlation at an unknown point in time using an extended functional delta method. Econom Theory 28(03):570–589MathSciNetCrossRefzbMATHGoogle Scholar
  24. Zhang X, Cheng G (2014) Bootstrapping high dimensional time series. ArXiv e-printsGoogle Scholar
  25. Zhou Z (2013) Heteroscedasticity and autocorrelation robust structural change detection. J Am Stat Assoc 108(502):726–740MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät StatistikTechnische Universität DortmundDortmundGermany
  2. 2.Ruhr Graduate School in EconomicsEssenGermany
  3. 3.Institut für Ökonometrie und StatistikUniversität zu KölnCologneGermany

Personalised recommendations