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

A residual-based multivariate constant correlation test

  • Fang Duan
  • Dominik WiedEmail author


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.


Structural breaks Hypothesis testing Correlation Residual effect 

JEL Classification

C12 C32 C58 



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


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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

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