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The power of some standard tests of stationarity against changes in the unconditional variance

  • Ibrahim Ahamada


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Mohamed Boutahar


    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - EHESS - École des hautes études en sciences sociales - CNRS - AMU - Aix-Marseille Université)

Abrupt changes in the unconditional variance of returns have been recently revealed in many empirical studies. In this paper, we show that traditional KPSS-based tests have a low power against nonstationarities stemming from changes in the unconditional variance. More precisely, we show that even under very strong abrupt changes in the unconditional variance, the asymptotic moments of the statistics of these tests remain unchanged. To overcome this problem, we use some CUSUM-based tests adapted for small samples. These tests do not compete with KPSS-based tests and can be considered as complementary. CUSUM-based tests confirm the presence of strong abrupt changes in the unconditional variance of stock returns, whereas KPSS-based tests do not. Consequently, traditional stationary models are not always appropriate to describe stock returns. Finally, we show how a model allowing abrupt changes in the unconditional variance is well appropriate for CAC 40 stock returns.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00476024.

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Date of creation: Apr 2010
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Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2010.28 - ISSN : 1955-611X. 2010
Handle: RePEc:hal:cesptp:halshs-00476024
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