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Tests for conditional ellipticity in multivariate GARCH models

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • M.D. Jiménez-Gamero

    (Département de statistiques et de recherche opérationnelle, Université de Séville, Séville, Espagne, Universidad de Sevilla = University of Seville)

  • S.G. Meintanis

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian Francq & M.D. Jiménez-Gamero & S.G. Meintanis, 2017. "Tests for conditional ellipticity in multivariate GARCH models," Post-Print hal-05417316, HAL.
    • Handle: RePEc:hal:journl:hal-05417316
    DOI: 10.1016/j.jeconom.2016.10.001
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    Cited by:

    1. is not listed on IDEAS
    2. Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    3. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    4. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    5. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    6. Simos Meintanis & Bojana Milošević & Marko Obradović & Mirjana Veljović, 2024. "Goodness‐of‐fit tests for the multivariate Student‐t distribution based on i.i.d. data, and for GARCH observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 298-319, March.
    7. Simos G. Meintanis & Joseph Ngatchou-Wandji & Šárka Hudecová, 2025. "Omnibus diagnostic procedures for vector multiplicative errors models," Statistical Papers, Springer, vol. 66(2), pages 1-44, February.
    8. 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.
    9. Aknouche, Abdelhakim & Francq, Christian, 2021. "Count And Duration Time Series With Equal Conditional Stochastic And Mean Orders," Econometric Theory, Cambridge University Press, vol. 37(2), pages 248-280, April.

    More about this item

    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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