Nam, Christopher F. H. (2013) The uncertainty of changepoints in time series. PhD thesis, University of Warwick.

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Abstract

Analysis concerning time series exhibiting changepoints have predominantly
focused on detection and estimation. However, changepoint estimates such as their
number and location are subject to uncertainty which is often not captured explicitly,
or requires sampling long latent vectors in existing methods. This thesis proposes
efficient, flexible methodologies in quantifying the uncertainty of changepoints.
The core proposed methodology of this thesis models time series and changepoints
under a Hidden Markov Model framework. This methodology combines existing
work on exact changepoint distributions conditional on model parameters with
Sequential Monte Carlo samplers to account for parameter uncertainty. The combination
of the two provides posterior distributions of changepoint characteristics in
light of parameter uncertainty.
This thesis also presents a methodology in approximating the posterior of
the number of underlying states in a Hidden Markov Model. Consequently, model
selection for Hidden Markov Models is possible. This methodology employs the use
of Sequential Monte Carlo samplers, such that no additional computational costs
are incurred from the existing use of these samplers.
The final part of this thesis considers time series in the wavelet domain, as opposed
to the time domain. The motivation for this transformation is the occurrence
of autocovariance changepoints in time series. Time domain modelling approaches
are somewhat limited for such types of changes, with approximations often taking
place. The wavelet domain relaxes these modelling limitations, such that autocovariance
changepoints can be considered more readily. The proposed methodology
develops a joint density for multiple processes in the wavelet domain which can
then be embedded within a Hidden Markov Model framework. Quantifying the
uncertainty of autocovariance changepoints is thus possible.
These methodologies will be motivated by datasets from Econometrics, Neuroimaging
and Oceanography.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Change-point problems, Time-series analysis
Official Date:	March 2013
Dates:	Date Event March 2013 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Aston, John A. D.
Extent:	x, 224 leaves : illustrations
Language:	eng

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