Abstract
Many aspects contribute to make financial markets one of the most challenging system to understand. The aim of this thesis is to study some aspects of their complexity by focusing on univariate e multivariate properties of log-returns time-series, namely multifractality and cross-dependence.In this thesis, we started by performing a thorough analysis of the scaling properties of synthetic time-series with different known scaling properties. This enabled us to do two things: find the presence of a strong bias in the estimation of the scaling exponents, and interpret measurement on real data which led us to uncover the true source of the multifractal behaviour of financial log-prices, which has been long debated in the literature. We addressed the presence of the bias by proposing a method which manages to filter out its presence and we validate it by applying it to synthetic time-series with known scaling properties and on empirical ones. We also found that this bias is due to the stability under aggregation of the log-returns which, due to their long memory, are processes which for high aggregation tend to a random variable which displays an exact multifractal scaling. Finally we focused the attention on linking the scaling properties of log-returns to their cross-correlation properties within a given market finding an intriguing non-linear relationship between the two quantities.
| Date of Award | 2018 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Tiziana Di Matteo (Supervisor) |