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

Preview

Text WRAP_THESIS_Zhang_2011.pdf - Submitted Version Download (4Mb) | Preview

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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Parameter estimation, Multiscale modeling, Time-series analysis
Date:	June 2011
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Publication Status:	Unpublished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
URI:	http://wrap.warwick.ac.uk/id/eprint/51576

Request changes to a record

Actions (login required)

View Item