Thesis supervisor: László Márkus
Location of studies (in Hungarian): ELTE, TTK, Matematikai Intézet, Valószínűségelméleti és Statisztika Tanszék Abbreviation of location of studies: ELTE
Description of the research topic:
A number of temporally evolving phenomena show evidences of non-linear dynamics. The character of the data obtained by observing such phenomena - and in particular the extremal behaviour - cannot be understood well by fitting the classical linear ARMA, or VAR models or analysing the spectral density. The theory of time series possesses, however, non-linear models, - the various generalisations of GARCH models, Threshold AutoRegressions (TAR), Markov or semi-Markov regime switching, just to mention a few,- that can be fitted to the mentioned data, eventually combined with linear models. The analysis of the interdependence structure and the properties e.g. roughness of the trajectories may provide help in choosing of the proper model. The non-linear interdependence structure of the process can be described by the autocopulas, while the trajectories can be characterised by the measure of their roughness, the fractal dimensions. The autocopulas and the fractal dimensions corresponding to various models are not known in many cases, so to determine them theoretically and understand the properties of their estimations are subject of current research. When the interdependence is described by autocopulas, the forecsat problem has to be revisited and elaborated anew. The fractal dimensions are proven to be a useful tool in various applications (hydrogeology, karstic systems) helping deeper understanding the processes of Nature. On the other hand the fractal dimension can be related to the Hurst coefficient, which entered common scientific knownledge as the measure of long memory. Gneiting and his collaborators showed examples that fractal dimension and the Hurst coefficient can be independent of each other, despite the fact that for affine invariant processes the relationship is one-to-one. The deeper understanding of the relationship of these two measures in the processes characterised by them is a goal of the suggested research as well as their effect to the magnitude and occurrence of extremal behaviour.
Required language skills: angol Number of students who can be accepted: 2
Deadline for application: 2016-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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