Javorsek, M;
(2015)
Modelling Multiple and Structured Oscillatory Phenomena.
Masters thesis , UCL (University College London).
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Abstract
This work deals with the modelling of multiple and structured oscillatory phenomena. The goal of the thesis is to show how stochastic oscillations can be modelled, and define their elliptical structures as a special class of bivariate time-dependant variation. The central part of the research is the introduction of new multivariate elliptical models and the review of existing definitions. The findings are presented in a table, where the classification is made based on whether the definitions are random or deterministic and whether they are defined in time or frequency domains. The previously introduced ellipse definitions for stochastic processes that have been described in the literature are limited to the frequency domain only. The main contribution of this work is in adding to existing time domain models by defining the description of the autocovariance ellipse and the forecast ellipse. Both of these definitions are non-random. The ellipses are defined from either the autocovariance or the forecast functions of the process as one moves forward in lag-time or forecast-time. In order to illustrate these theoretical concepts and show the usefulness of the new definition we investigate these concepts using a parametric model. Univariate and bivariate, real-valued and complex-valued models are considered, and their representation discussed. The richest model proposed is that of a complex-valued bivariate autoregressive process of order one and this is based on modelling using affine transformation matrices. This model results in a stochastic oscillation and the elliptical definitions proposed are explored in this context. The actual behaviour of the proposed stochastic process is also illustrated on simulated data. Some limitations of this approach are discussed and extensions of this model are presented.
| Type: | Thesis (Masters) |
|---|---|
| Title: | Modelling Multiple and Structured Oscillatory Phenomena |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Keywords: | Statistics, Time series, Oscillations |
| UCL classification: | UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1471338 |
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