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Non-linear dependences in finance
Statistical Finance · Submitted 18 Sep 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The thesis is composed of three parts. | background 0.70 | 0.25 | 0.01 | asserted 1.00 |
| s1 | 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. | background 0.53 | 0.20 | 0.02 | asserted 0.99 |
| s2 | I propose two extensions of usual tests when dependence is present in the sample data and when observations have a fat-tailed distribution. | contribution 0.96 | 0.92 | 0.05 | asserted 0.99 |
| s3 | The financial content of the thesis starts in Part II. | background 0.71 | 0.17 | 0.02 | asserted 0.99 |
| s4 | 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. | contribution 0.97 | 0.90 | 0.04 | asserted 0.95 |
| s5 | A calibration of a new factor model is presented here, together with a comparison to measurements on real data. | contribution 0.85 | 0.90 | 0.04 | asserted 0.99 |
| s6 | Finally, Part III investigates the temporal dependences of single time series, using the same tools and measures of correlation. | contribution 0.67 | 0.63 | 0.03 | asserted 0.99 |
| s7 | 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. | contribution 1.00 | 0.94 | 0.13 | asserted 0.99 |
| s8 | The latter can be formulated model-free and is not specific to financial time series. | interpretation 0.78 | 0.66 | 0.06 | asserted 1.00 |
| s9 | 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. | contribution 0.84 | 0.92 | 0.09 | asserted 1.00 |
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Original abstract
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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3 arXiv papers cite this in 4 sentences
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This is the main purposes of the theory of robust estimators [ref] where the RMT regime $N ≍T$ has been subject to a lot studies in the past few years, especially in the case of elliptical distributions [ref] .
Cleaning large correlation matrices: tools from random matrix theory · Distribution of the data entries · 0.91
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