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The Power of some Standard tests of stationarity against changes in the unconditional variance

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Abstract

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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  • Ibrahim Ahamada & Mohamed Boutahar, 2010. "The Power of some Standard tests of stationarity against changes in the unconditional variance," Documents de travail du Centre d'Economie de la Sorbonne 10028, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:10028
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    Keywords

    KPSS test; panel stationarity test; unconditional variance; abrupt changes; stock returns; size-power curve;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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