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Tests for conditional ellipticity in multivariate GARCH models

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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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    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. 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.

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    More about this item

    Keywords

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