Zhang, Fan (Researcher in mathematics) (2011) Parameter estimation and model fitting of stochastic processes. PhD thesis, University of Warwick.

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Abstract

Multiscale methods such as averaging and homogenization have become an increasingly
interesting topic in stochastic time series modelling. When applying the averaged/
homogenized processes to applications such as parameter estimation and filtering
problems, the resulting asymptotic properties are often weak. In this thesis, we focus on
the above mentioned multiscale methods applied on Ornstein-Uhlenbeck processes. We
find that the maximum likelihood based estimators for the drift and diffusion parameters
derived from the averaged/homogenized systems can use the corresponding marginal multiscale
data as observations, and still provide a strong convergence to the true value as
if the observations are from the averaged/homogenized systems themselves. The asymptotic
distribution for the estimators are studied in this thesis for the averaging problem,
while that of the homogenization problem exhibit more difficulties and will be an interest
of future work. In the case when applying the multiscale methods to the Kalman filter of
Ornstein-Uhlenbeck systems, we study the convergence between the marginal covariance
and marginal mean of the full scale system and those of the averaged/homogenized systems,
by measuring their discrepancies.
In Part III, we study real world projects of time series modelling in the field of
econometrics. Chapter 7 presents a modelling project on interest rate time series from the
well known Nelson-Siegel yield curve model. The methodology shows a development from
standard Vector Autoregressive model to Bayesian based heteroscedastic regression model.
Gibbs sampling is used as theMonte Carlo method. Chapter 8 presents a model comparison
in modelling a portfolio of economic indices between constant correlation GARCH and
Dynamic Conditional Correlation GARCH models. It compares the two models suitability
in capturing the effect of "volatility clustering".

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Parameter estimation, Multiscale modeling, Time-series analysis
Official Date:	June 2011
Dates:	Date Event June 2011 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute ; Centre for Scientific Computing
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Stuart, A. M. ; Papavasiliou, Anastasia, 1975-
Sponsors:	University of Warwick
Extent:	viii, 154 pages : charts
Language:	eng

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