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Tests for sphericity in multivariate garch models

Author

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  • Francq, Christian
  • Jiménez Gamero, Maria Dolores
  • Meintanis, Simos

Abstract

Tests for spherical symmetry of the innovation distribution are proposed in multivariate GARCH models. The new tests are of Kolmogorov--Smirnov and Cram\'er--von Mises--type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. It is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of the innovations. Therefore a conditional Monte Carlo procedure is used to actually carry out the tests. The validity of this resampling scheme is formally justified. Results on the behavior of the test in finite--samples are included, as well as an application on financial data.

Suggested Citation

  • Francq, Christian & Jiménez Gamero, Maria Dolores & Meintanis, Simos, 2015. "Tests for sphericity in multivariate garch models," MPRA Paper 67411, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67411
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    File URL: https://mpra.ub.uni-muenchen.de/67411/1/MPRA_paper_67411.pdf
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    References listed on IDEAS

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    Cited by:

    1. Francq, Christian & Zakoian, Jean-Michel, 2015. "Joint inference on market and estimation risks in dynamic portfolios," MPRA Paper 68100, University Library of Munich, Germany.

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    More about this item

    Keywords

    Extended CCC-GARCH; Spherical symmetry; Empirical characteristic function; Conditional Monte Carlo test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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