Bayesian estimation of self-similarity exponent

Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2012

Author dc:creator

• Makarava, Natallia

Contributors dc:contributor

• Holschneider, Matthias

• Hurst-Exponent
• Bayessche Statistik
• fraktionale Brown'schen Bewegung
• fraktionales Gauß'sches Rauschen
• fixierte Augenbewegungen
• Hurst exponent
• Bayesian inference
• fractional Brownian motion
• fractional Gaussian noise
• fixational eye movements

Statement dc:rights

• Keine öffentliche Lizenz: Unter Urheberrechtsschutz

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/6175

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:6175