Parameter estimation and model fitting of stochastic processes
Zhang, Fan (Researcher in mathematics) (2011) Parameter estimation and model fitting of stochastic processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2585153~S1
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|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute ; Centre for Scientific Computing|
|Supervisor(s)/Advisor:||Stuart, A. M. ; Papavasiliou, Anastasia, 1975-|
|Sponsors:||University of Warwick|
|Extent:||viii, 154 pages : charts|
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