Hostname: page-component-89b8bd64d-4ws75 Total loading time: 0 Render date: 2026-05-06T07:27:39.968Z Has data issue: false hasContentIssue false
  • English
  • Français

TESTING FOR A CHANGE IN CORRELATION AT ANUNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONALDELTA METHOD

Published online by Cambridge University Press:  25 November 2011

Dominik Wied ,
Walter Krämer  and
Herold Dehling
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a new test against a change in correlationat an unknown point in time based on cumulated sumsof empirical correlations. The test does not requirethat inputs are independent and identicallydistributed under the null. We derive its limitingnull distribution using a new functional deltamethod argument, provide a formula for its localpower for particular types of structural changes,give some Monte Carlo evidence on its finite-samplebehavior, and apply it to recent stock returns.

Information

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 3 , June 2012 , pp. 570 - 589
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Financial support by DeutscheForschungsgemeinschaft (SFB 823, Statistiknichtlinearer dynamischer Prozesse) is gratefullyacknowledged. We are grateful to the co-editorBenedikt M. Pötscher, three anonymous referees,Matthias Arnold, Roland Fried, Werner Ploberger,Christoph Rothe, Tatiana Vlasenco, Daniel Vogel,and Henryk Zähle for helpful criticism andcomments.

References

REFERENCES

Andrews, D. (1997) A conditional Kolmogorov test. Econometrica 65, 1097–1128.CrossRefGoogle Scholar
Aue, A., Hörmann, S., Horvath, L., & Reimherr, M. (2009) Break detection in the covariance structure of multivariate time series models. Annals of Statistics 37, 4046–4087.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Carrasco, M. & Chen, X. (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17–39.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
Davis, R. & Mikosch, T. (1998) The sample autocorrelations of heavy-tailed processes with applications to ARCH. Annals of Statistics 26, 2049–2080.CrossRefGoogle Scholar
De Jong, R. & Davidson, J. (2000) Consistency of kernel estimators of heteroscedastic and autocorrelated covariance matrices. Econometrica 68, 407–424.CrossRefGoogle Scholar
Dias, A. & Embrechts, P. (2004) Change point analysis for dependence structures in finance and insurance. In Szegö, G. (ed.), Risk Measures of the 21th Century, pp. 321–335. Wiley.Google Scholar
Forbes, K. & Rigobon, R. (2002) No contagion, only interdependence: Measuring stock market comovements. Journal of Finance 57, 2223–2261.CrossRefGoogle Scholar
Galeano, P. & Peña, D. (2007) Covariance changes detection in multivariate time series. Journal of Statistical Planning and Inference 137, 194–211.CrossRefGoogle Scholar
Gill, R. (1989) Non- and semi-parametric maximum likelihood estimators and the von Mises method—Part 1. Scandinavian Journal of Statistics 16, 97–128.Google Scholar
Goetzmann, W., Li, L., & Rouwenhorst, K. (2005) Long-term global market correlations. Journal of Business 78, 1–38.CrossRefGoogle Scholar
Hansen, B. (1991) GARCH(1,1) processes are near-epoch dependent. Economics Letters 36, 181–186.CrossRefGoogle Scholar
Inoue, A. (2001) Testing for distributional change in time series. Econometric Theory 17, 156–187.CrossRefGoogle Scholar
Jennrich, R. (1970) An asymptotic chi-square test for the equality of two correlation matrices. Journal of the American Statistical Association 65, 904–912.Google Scholar
Kiefer, J. (1959) K-sample analogues of the Kolmogorov-Smirnov and Cramér-V. Mises Tests. Annals of Mathematical Statistics 30, 420–447.CrossRefGoogle Scholar
Krämer, W. (2002) Statistische Besonderheiten von Finanzzeitreihen. Jahrbücher für National-ökonomie und Statistik 222, 210–229.CrossRefGoogle Scholar
Krämer, W. & Schotman, P. (1992) Range vs. maximum in the OLS-based version of the CUSUM test. Economics Letters 40, 379–381.CrossRefGoogle Scholar
Krishan, C., Petkova, R., & Ritchken, P. (2009) Correlation risk. Journal of Empirical Finance 16, 353–367.CrossRefGoogle Scholar
Longin, F. & Solnik, B. (1995) Is the correlation in international equity returns constant: 1960–1990? International Money and Finance 14, 3–26.CrossRefGoogle Scholar
McAleer, M., Chan, F., Hoti, S., & Lieberman, O. (2008) Generalized autoregressive conditional correlation. Econometric Theory 24, 1554–1583.CrossRefGoogle Scholar
Pearson, E. & Wilks, S. (1933) Methods of statistical analysis appropriate for k samples of two variables. Biometrika 25, 353–378.CrossRefGoogle Scholar
Ploberger, W. & Krämer, W. (1990) The local power of the CUSUM and CUSUM of squares tests. Econometric Theory 6, 335–347.CrossRefGoogle Scholar
Ploberger, W. & Krämer, W. (1992) The CUSUM-test with OLS residuals. Econometrica 60, 271–285.CrossRefGoogle Scholar
Ploberger, W., Krämer, W., & Kontrus, K. (1989) A new test for structural stability in the linear regression model. Journal of Econometrics 40, 307–318.CrossRefGoogle Scholar
Rothe, C. & Wied, D. (2011) Misspecification Testing in a Class of Conditional Distributional Models. SFB 823 Discussion paper, TU Dortmund.CrossRefGoogle Scholar
Scheffler, H.-P. & Meerschaert, M. (2001) Sample cross-correlations for moving averages with regularly varying tails. Journal of Time Series Analysis 22, 481–492.Google Scholar
Schmid, F., Schmidt, R., Blumentritt, T., Gaissler, S., & Ruppert, M. (2010) Copula-based measures of multivariate association. In Durante, F., Härdle, W., Jaworski, P., & Rychlik, T. (eds.), Workshop on Copula Theory and Its Applications, pp. 209–236. Springer-Verlag.CrossRefGoogle Scholar
van der Vaart, A. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar
Wooldridge, J. & White, H. (1988) Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4, 210–230.CrossRefGoogle Scholar