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On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests

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  • Naâmane Laïb
  • Mohamed Lemdani
  • Elias Ould‐Saïd

Abstract

. Considering the generalized autoregressive conditionally heteroskedastic with stochastic mean (GARCH‐SM) model, we establish in this article the consistency and the weak representation of a functional of its residual empirical process. Based on this result, a symmetry test for GARCH‐SM model is developed. Simulations are given to show the asymptotic behaviour and normality of the test statistic.

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  • Naâmane Laïb & Mohamed Lemdani & Elias Ould‐Saïd, 2008. "On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 762-782, September.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:5:p:762-782
    DOI: 10.1111/j.1467-9892.2008.00580.x
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    References listed on IDEAS

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    4. Winfried Stute, 2001. "Residual analysis for ARCH(p)-time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 393-403, December.
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    6. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
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    Cited by:

    1. Laïb Naâmane & Lemdani Mohamed & Ould Saïd Elias, 2013. "A functional conditional symmetry test for a GARCH-SM model: Power asymptotic properties," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 75-104, March.

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