Skip to main content
SpringerLink
Log in

A new fluctuation test for constant variances with applications to finance

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

We present a test to determine whether variances of time series are constant over time. The test statistic is a suitably standardized maximum of cumulative first and second moments. We apply the test to time series of various assets and find that the test performs well in applications. Moreover, we propose a portfolio strategy based on our test which hedges against potential financial crises and show that it works in practice.

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

Similar content being viewed by others

References

  • Andreou E, Ghysels E (2002) Detecting multiple breaks in financial market volatility dynamics. J Appl Econom 17: 579–600

    Article  Google Scholar 

  • Andreou E, Ghysels E (2006) Monitoring disruptions in financial markets. J Econom 135: 77–124

    Article  MathSciNet  Google Scholar 

  • Andreou E, Ghysels E (2010) Structural breaks in financial time series. In: Andersen T, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of financial time series. Springer, Berlin

    Google Scholar 

  • Andrews DWK (1997) A conditional Kolmogorov test. Econometrica 65(5): 1097–1128

    Article  MathSciNet  MATH  Google Scholar 

  • Aue A, Hörmann S, Horváth L, Reimherr M (2009) Break detection in the covariance structure of multivariate time series models. Ann Stat 37(6B): 4046–4087

    Article  MATH  Google Scholar 

  • Billingsley P (1968) Convergence of probability measures. Wiley, New York

    MATH  Google Scholar 

  • Bissantz N, Steinorth V, Ziggel D (2011) Stabilität von Diversifikationseffekten im Markowitz-Modell. AStA Wirtschafts- und Sozialstatistisches Archiv 5(2): 145–157

    Article  Google Scholar 

  • Campbell R, Forbes C, Koedijk K, Kofman P (2008) Increasing correlations or just fat tails?. J Empir Finance 15: 287–309

    Article  Google Scholar 

  • Carrasco M, Chen XH (2002) Mixing and moment properties of various garch and stochastic volatility models. Econom Theory 18: 17–39

    Article  MathSciNet  MATH  Google Scholar 

  • Chen J, Gupta AK (1997) Testing and locating variance changepoints with application to stock prices. J Am Stat Assoc 92: 739–747

    Article  MathSciNet  MATH  Google Scholar 

  • Chu C-SJ, Stinchcombe M, White H (1996) Monitoring structural change. Econometrica 64(5): 1045–1065

    Article  MATH  Google Scholar 

  • Chu CS (1995) Detecting parameter shift in GARCH models. Econom Rev 14: 241–266

    Article  MATH  Google Scholar 

  • Davidson J (1994) Stochastic limit theory. Oxford University Press, Oxford

    Book  Google Scholar 

  • Davidson J, de Jong RM (2000) Consistency of kernel estimators of heteroscedastic and autocorrelated covariance matrices. Econometrica 68(2): 407–424

    Article  MathSciNet  MATH  Google Scholar 

  • Dias A, Embrechts P (2004) Change point analysis for dependence structures in finance and insurance. In: Szegö G (ed) Risk measures of the 21st century. Wiley, New York, pp 321–335

    Google Scholar 

  • Galeano P, Peña D (2007) Covariance changes detection in multivariate time series. J Stat Plan Inference 137(1): 194–211

    Article  MATH  Google Scholar 

  • Goetzmann WN, Li L, Rouwenhorst KG (2005) Long-term global market correlations. J Bus 78(1): 1–38

    Article  Google Scholar 

  • Hansen BE (1991) GARCH(1,1) processes are near-epoch dependent. Econ Lett 36: 181–186

    Article  MATH  Google Scholar 

  • Inoue A (2001) Testing for distributional change in time series. Econom Theory 17: 156–187

    Article  MATH  Google Scholar 

  • Jennrich RI (1970) An asymptotic chi-square test for the equality of two correlation matrices. J Am Stat Assoc 65: 904–912

    MathSciNet  MATH  Google Scholar 

  • Kokoszka P, Leipus R (2000) Change-point estimation in ARCH models. Bernoulli 6: 513–539

    Article  MathSciNet  MATH  Google Scholar 

  • Krishan CNV, Petkova R, Ritchken P (2009) Correlation risk. J Empir Finance 16: 353–367

    Article  Google Scholar 

  • Krämer W, Schotman P (1992) Range vs. maximum in the OLS-based version of the CUSUM test. Econ Lett 40: 379–381

    Article  MATH  Google Scholar 

  • Longin F, Solnik B (2002) Extreme correlation of international equity markets. J Finance 56: 649–675

    Article  Google Scholar 

  • Mikosch T, Starica C (2004) Changes of structure in financial time series and the GARCH model. Revstat Stat J 2: 41–73

    MathSciNet  MATH  Google Scholar 

  • Pearson ES, Wilks SS (1933) Methods of statistical analysis appropriate for k samples of two variables. Biometrika 25: 353–378

    Google Scholar 

  • Ploberger W, Krämer W (1990) The local power of the CUSUM and CUSUM of squares tests. Econom Theory 6: 335–347

    Article  Google Scholar 

  • Ploberger W, Krämer W (1992) The CUSUM-test with OLS residuals. Econometrica 60(2): 271–285

    Article  MathSciNet  MATH  Google Scholar 

  • Ploberger W, Krämer W, Kontrus K (1989) A new test for structural stability in the linear regression model. J Econom 40: 307–318

    Article  MATH  Google Scholar 

  • Wied D, Krämer W, Dehling H (2011) Testing for a change in correlation at an unknown point in time using an extended functional delta method. Econom Theory, forthcoming

Download references

Author information

Authors and Affiliations

  1. Fakultät Statistik, TU Dortmund, 44221, Dortmund, Germany

    Dominik Wied & Matthias Arnold

  2. Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany

    Nicolai Bissantz

  3. quasol GmbH, Marktallee 8, 48165, Münster, Germany

    Daniel Ziggel

Authors
  1. Dominik Wied
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthias Arnold
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicolai Bissantz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daniel Ziggel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dominik Wied.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wied, D., Arnold, M., Bissantz, N. et al. A new fluctuation test for constant variances with applications to finance. Metrika 75, 1111–1127 (2012). https://doi.org/10.1007/s00184-011-0371-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-011-0371-7

Keywords

Search

Navigation