Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter (A) March 6, 2013

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

  • Naâmane Laïb , Mohamed Lemdani and Elias Ould Saïd


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.

* 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

© by Oldenbourg Wissenschaftsverlag, München, Germany

Downloaded on 4.10.2023 from
Scroll to top button