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The main aim of this volume is to present key recent developments in the fields of modelling structural breaks, and the analysis of long memory and stock market volatility.

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We perform a comprehensive Monte Carlo comparison between nine procedures available in the literature to detect jumps in financial assets proposed by Barndorff-Nielsen and Shephard (2006), Andersen et al. (2007), Lee and Mykland (2008), Aït-Sahalia and Jacod (2008), Jiang and Oomen (2008), Andersen et al. (2009) (two tests), Corsi et al. (2010) and Podolskij and Ziggel (2010). We evaluate size and power properties of the procedures under alternative sampling frequencies, levels of volatility, persistence in volatility, degree of contamination with microstructure noise, jump size and intensity. The overall best performance is showed by the Lee and Mykland (2008) and Andersen et al. (2007) intraday procedures, provided the price process is not not very volatile. We propose an improvement to these procedures based on critical values obtained from finite sample approximations of the distribution of the test statistics. We show the validity to use reunion and intersection across procedures and across sampling frequencies for potential users of the tests to minimize spurious jump detection. Finally, we report an empirical analysis using real high frequency data on five stocks listed in the New York Stock Exchange.

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