dc.contributor.author | Alokley, Sara Ali | |
dc.date.accessioned | 2015-07-20T09:02:40Z | |
dc.date.issued | 2015-04-08 | |
dc.description.abstract | In this thesis we present a numerical and analytical study of modelling extremes in chaotic
dynamical systems. We study a range of examples with different dependency structures,
and different clustering characteristics. We compare our analysis to the extreme statistics
observed for financial returns data, and hence consider the modelling potential of using
chaotic systems for understanding financial returns. As part of the study we use the
block maxima approach and the peak over threshold method to compute the distribution
parameters that arise in the corresponding extreme value distributions. We compare
these computations to the theoretical answers, and moreover we obtain error bounds on
the rate of convergence of these schemes. In particular we investigate the optimal block
size when applying the block maxima method. Since the time series of observations on a
dynamical system have dependency we must therefore go beyond the classic approach of
studying extremes for independent identically distributed random variables. This is the
main purpose of our study. As part of this thesis, we also study clustering in financial
returns, and again investigate the potential of using dynamical systems models. Moreover
we can also compare numerical quantification of clustering with theoretical approaches. As
further work, we measure the dependency structures in our models using a rescaled range
analysis. We also make preliminary investigations into record statistics for dynamical
systems models, and relate our findings to record statistics in financial data, and to other
models (such as random walk models). | en_GB |
dc.description.sponsorship | King Faisal University | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/17935 | |
dc.language.iso | en | en_GB |
dc.publisher | University of Exeter | en_GB |
dc.relation.source | Yahoo Finance | en_GB |
dc.subject | Extremes | en_GB |
dc.subject | Financial Return | en_GB |
dc.subject | Records | en_GB |
dc.subject | Hurst Exponent | en_GB |
dc.subject | Dynamical System | en_GB |
dc.title | Understanding Extremes and Clustering in Chaotic Maps and Financial Returns Data | en_GB |
dc.type | Thesis or dissertation | en_GB |
dc.date.available | 2015-07-20T09:02:40Z | |
dc.contributor.advisor | Holland, Mark | |
dc.contributor.advisor | Harris, Richard | |
dc.publisher.department | Mathematics | en_GB |
dc.publisher.department | Business School | en_GB |
dc.type.degreetitle | PhD in Financial Mathematics | en_GB |
dc.type.qualificationlevel | Doctoral | en_GB |
dc.type.qualificationname | PhD | en_GB |