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In addition to testing for the presence of breaks, the statistics identify the number and location of multiple breaks. We study the size and power of the new tests for detecting breaks in the conditional variance under various realistic univariate heteroscedastic models, change\u2010point hypotheses and sampling schemes. The paper concludes with an empirical analysis using data from the stock and FX markets for which we find multiple breaks associated with the Asian and Russian financial crises. These events resulted in changes in the dynamics of volatility of asset returns in the samples prior and post the breaks. 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