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When is a copula constant? A test for changing relationships

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  • Busetti, F.
  • Harvey, A.

Abstract

A copula defines the probability that observations from two time series lie below given quantiles. It is proposed that stationarity tests constructed from indicator variables be used to test against the hypothesis that the copula is changing over time. Tests associated with different quantiles may point to changes in different parts of the copula, with the lower quantiles being of particular interest in financial applications concerned with risk. Tests located at the median provide an overall test of a changing relationship. The properties of various tests are compared and it is shown that they are still effective if pre-filtering is carried out to correct for changing volatility or, more generally, changing quantiles. Applying the tests to daily stock return indices in Korea and Thailand over the period 1995-9 indicates that the relationship between them is not constant over time.

Suggested Citation

  • Busetti, F. & Harvey, A., 2008. "When is a copula constant? A test for changing relationships," Cambridge Working Papers in Economics 0841, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0841
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    References listed on IDEAS

    as
    1. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    2. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge.
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    9. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, vol. 87(1), pages 167-189, August.
    10. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    11. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.
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    More about this item

    Keywords

    Concordance; quantile; rank correlation; stationarity test; tail dependence.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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