Use this URL to cite or link to this record in EThOS:
Title: Modelling data using continuous time autoregressions
Author: Giannopoulos, P.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2006
Availability of Full Text:
Full text unavailable from EThOS.
Please contact the current institution’s library for further details.
This dissertation is concerned with continuous-time autoregressive (CAR) processes and their estimation using Bayesian techniques. First, the Bayesian approach to time series modelling is described, then established methods in the literature for estimating CAR processes are reviewed. The first problem that is addressed is that of estimating the CAR model parameters from discrete-time noisy observations when the model order P is known. Observations can be uniformly or non-uniformly sampled unlike discrete-time models where observations have to be uniform. A deterministic method is initially proposed that consists of an iterative least-squares (LS) algorithm which uses the output of the Kalman smoother as an estimate of the derivatives up to order (P-1). The Pth order derivative is approximated by a difference operator. The Kalman filter is then run with those parameters and the process is repeated until convergence. A bias in the parameter estimation is unavoidable for finite sampling interval and sample size. Results are compared to existing deterministic methods. The problem is then cast into a Bayesian framework. The posterior distribution is not analytical tractable, therefore we resort to Markov chain Monte Carlo (MCMC) methods for simulating samples from the required distributions. A proposed based on the LS estimate is developed and combined with the random walk proposal to have a few successive samples drawn from each proposal. Performance is quantified in terms of the autocorrelation function. The more general case of data originating from a process of unknown order is then considered. Classical model selection criteria are defined in terms of the goodness of fit plus a penalty factor which penalizes complex models compared to simpler ones. As model selection is not the ultimate goal of our research, we resort to MCMC techniques. In particular, the reversible-jump MCMC method, which can move between models of different dimensionality in a flexible way, is used. A partial and a full-vector proposal are used and simulation results are presented. Results are compared to classical model selection techniques. We use the CAR process for restoring audio recordings and speech segments that are corrupted by broadband noise is tackled. The problem of click noise is also tackled.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available