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A Model Specification Test For GARCH(1,1) Processes

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  • Anne Leucht
  • Jens-Peter Kreiss
  • Michael H. Neumann

Abstract

type="main" xml:id="sjos12158-abs-0001"> We provide a consistent specification test for generalized autoregressive conditional heteroscedastic (GARCH (1,1)) models based on a test statistic of Cramér-von Mises type. Because the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based (semiparametric) bootstrap method to approximate critical values of the test and to verify its asymptotic validity. Finally, we illuminate the finite sample behaviour of the test by some simulations.

Suggested Citation

  • Anne Leucht & Jens-Peter Kreiss & Michael H. Neumann, 2015. "A Model Specification Test For GARCH(1,1) Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1167-1193, December.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:1167-1193
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    References listed on IDEAS

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    Cited by:

    1. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    2. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for a class of multivariate asymmetric power GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 964-1002, November.
    3. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    4. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for the asymmetric power GARCH model when the power is unknown," Statistical Papers, Springer, vol. 63(3), pages 755-793, June.
    5. Šárka Hudecová & Marie Hušková & Simos G. Meintanis, 2021. "Goodness–of–Fit Tests for Bivariate Time Series of Counts," Econometrics, MDPI, vol. 9(1), pages 1-20, March.
    6. Michael H. Neumann, 2021. "Bootstrap for integer‐valued GARCH(p, q) processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 343-363, August.
    7. Christian Francq & Olivier Wintenberger & Jean-Michel Zakoïan, 2018. "Goodness-of-fit tests for Log-GARCH and EGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 27-51, March.
    8. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.

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