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Non-linear dependences in finance

  • R\'emy Chicheportiche
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    The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I propose two extensions of usual tests when dependence is present in the sample data and when observations have a fat-tailed distribution. The financial content of the thesis starts in Part II. I present there my studies regarding the "cross-sectional" dependences among the time series of daily stock returns, i.e. the instantaneous forces that link several stocks together and make them behave somewhat collectively rather than purely independently. A calibration of a new factor model is presented here, together with a comparison to measurements on real data. Finally, Part III investigates the temporal dependences of single time series, using the same tools and measures of correlation. I propose two contributions to the study of the origin and description of "volatility clustering": one is a generalization of the ARCH-like feedback construction where the returns are self-exciting, and the other one is a more original description of self-dependences in terms of copulas. The latter can be formulated model-free and is not specific to financial time series. In fact, I also show here how concepts like recurrences, records, aftershocks and waiting times, that characterize the dynamics in a time series can be written in the unifying framework of the copula.

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    File URL: http://arxiv.org/pdf/1309.5073
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    Paper provided by arXiv.org in its series Papers with number 1309.5073.

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    Date of creation: Sep 2013
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    Handle: RePEc:arx:papers:1309.5073
    Contact details of provider: Web page: http://arxiv.org/

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    1. Vincenzo Tola & Fabrizio Lillo & Mauro Gallegati & Rosario N. Mantegna, 2005. "Cluster analysis for portfolio optimization," Papers physics/0507006, arXiv.org.
    2. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
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