eprintid: 1471338
rev_number: 26
eprint_status: archive
userid: 608
dir: disk0/01/47/13/38
datestamp: 2015-12-10 12:31:56
lastmod: 2019-10-19 07:16:59
status_changed: 2015-12-10 12:31:56
type: thesis
metadata_visibility: show
creators_name: Javorsek, M
title: Modelling Multiple and Structured Oscillatory Phenomena
ispublished: unpub
divisions: A01
divisions: B04
divisions: C06
divisions: F61
keywords: Statistics, Time series, Oscillations
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.
date: 2015-10-28
date_type: published
oa_status: green
full_text_type: other
thesis_class: doctoral_open
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1055259
language_elements: English
lyricists_name: Javorsek, Marko
lyricists_id: MJAVO51
actors_name: Javorsek, Marko
actors_id: MJAVO51
actors_role: owner
full_text_status: public
pages: 112
event_title: UCL (University College London)
institution: UCL (University College London)
department: Statistical Science
thesis_type: Masters
citation:        Javorsek, M;      (2015)    Modelling Multiple and Structured Oscillatory Phenomena.                   Masters thesis , UCL (University College London).     Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1471338/1/MPhill%20thesis_MJ_v2.pdf