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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 30, Issue 1


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

Naâmane Laïb / Mohamed Lemdani / Elias Ould Saïd
Published Online: 2013-03-06 | DOI: https://doi.org/10.1524/strm.2012.1082


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.

Keywords: Contiguity; GARCH-SM model; goodness-of-fit; local power; residual law

About the article

* Correspondence address: Univ. de Lille 2, Lab. Biomaths., 3, rue du Professeur Laguesse, 59006 Lille, Frankreich,

Published Online: 2013-03-06

Published in Print: 2013-03-01

Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 30, Issue 1, Pages 75–104, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2012.1082.

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