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A functional conditional symmetry test for a GARCH-SM model: Power asymptotic properties

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  • Laïb Naâmane
  • Lemdani Mohamed
  • Ould Saïd Elias

Abstract

In this paper we consider the empirical process of the errors appearing in a generalized autoregressive conditional heteroskedastic with stochastic mean (GARCH-SM) model. Various functional tests of conditional symmetry can be built on the basis of the limiting distribution of this process. In particular, a Cramér–von Mises-type test is considered. Its theoretical power is studied under fixed and local alternatives. Using the Karhunen–Loève decomposition, the limiting law of the latter is approximated by a chi-square distribution under both null and alternative hypotheses. The local power under a sequence of alternatives is also computed.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:strimo:v:30:y:2013:i:1:p:75-104:n:1
    DOI: 10.1524/strm.2012.1082
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    References listed on IDEAS

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