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Tests for conditional ellipticity in multivariate GARCH models

Author

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  • Francq, C.
  • Jiménez-Gamero, M.D.
  • Meintanis, S.G.

Abstract

Tests are proposed for the assumption that the conditional distribution of a multivariate GARCH process is elliptic. These tests are of Kolmogorov–Smirnov and Cramér–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 new tests in finite-samples are included along with comparisons with other tests.

Suggested Citation

  • Francq, C. & Jiménez-Gamero, M.D. & Meintanis, S.G., 2017. "Tests for conditional ellipticity in multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 196(2), pages 305-319.
  • Handle: RePEc:eee:econom:v:196:y:2017:i:2:p:305-319
    DOI: 10.1016/j.jeconom.2016.10.001
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    References listed on IDEAS

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    Cited by:

    1. Karanasos, Menelaos & Xu, Yongdeng, 2017. "Matrix Inequality Constraints for Vector (Asymmetric Power) GARCH/HEAVY Models and MEM with spillovers: some New (Mixture) Formulations," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    2. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    3. Donghang Luo & Ke Zhu & Huan Gong & Dong Li, 2020. "Testing error distribution by kernelized Stein discrepancy in multivariate time series models," Papers 2008.00747, arXiv.org.
    4. Francq, Christian & Zakoian, Jean-Michel, 2019. "Testing the existence of moments for GARCH processes," MPRA Paper 98892, University Library of Munich, Germany.
    5. Aknouche, Abdelhakim & Francq, Christian, 2018. "Count and duration time series with equal conditional stochastic and mean orders," MPRA Paper 90838, University Library of Munich, Germany.

    More about this item

    Keywords

    MGARCH; Spherical symmetry; Empirical characteristic function; Conditional Monte Carlo test; Extended CCC-GARCH;

    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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