Estimating generalized state density of near-extreme events and its applications in analyzing stock data |
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Authors: | Jin-Guan Lin Chao Huang Li-Ping Zhu |
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Institution: | a Department of Mathematics, Southeast University, Nanjing 210096, China b School of Finance and Statistics, East China Normal University, Shanghai 200241, China |
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Abstract: | This paper studies the generalized state density (GDOS) of near-historical extreme events of a set of independent and identically distributed (i.i.d.) random variables. The generalized density of states is proposed which is defined as a probability density function (p.d.f.). For the underlying distribution in the domain of attraction of the three well-known extreme value distribution families, we show the approximate form of the mean GDOS. Estimates of the mean GDOS are presented when the underlying distribution is unknown and the sample size is sufficiently large. Some simulations have been performed, which are found to agree with the theoretical results. The closing price data of the Dow-Jones industrial index are used to illustrate the obtained results. |
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Keywords: | Extreme value statistics Domains of attraction Density of states Generalized density of near-extreme events Kernel density estimate |
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