Estimation of a class of nonlinear time series models.

Sando, Simon Andrew (2004) Estimation of a class of nonlinear time series models. PhD thesis, Queensland University of Technology.

Abstract

The estimation and analysis of signals that have polynomial phase and constant or time-varying amplitudes with the addititve noise is considered in this dissertation.Much work has been undertaken on this problem over the last decade or so, and there are a number of estimation schemes available. The fundamental problem when trying to estimate the parameters of these type of signals is the nonlinear characterstics of the signal, which lead to computationally difficulties when applying standard techniques such as maximum likelihood and least squares. When considering only the phase data, we also encounter the well known problem of the unobservability of the true noise phase curve.

The methods that are currently most popular involve differencing in phase followed by regression, or nonlinear transformations. Although these methods perform quite well at high signal to noise ratios, their performance worsens at low signal to noise, and there may be significant bias. One of the biggest problems to efficient estimation of these models is that the majority of methods rely on sequential estimation of the phase coefficients, in that the highest-order parameter is estimated first, its contribution removed via demodulation, and the same procedure applied to estimation of the next parameter and so on. This is clearly an issue in that errors in estimation of high order parameters affect the ability to estimate the lower order parameters correctly. As a result, stastical analysis of the parameters is also difficult.

In thie dissertation, we aim to circumvent the issues of bias and sequential estiamtion by considering the issue of full parameter iterative refinement techniques. ie. given a possibly biased initial estimate of the phase coefficients, we aim to create computationally efficient iterative refinement techniques to produce stastically efficient estimators at low signal to noise ratios. Updating will be done in a multivariable manner to remove inaccuracies and biases due to sequential procedures.

Stastical analysis and extensive simulations attest to the performance of the schemes that are presented, which include likelihood, least squares and bayesian estimation schemes. Other results of importance to the full estimatin problem, namely when there is error in the time variable, the amplitude is not constant, and when the model order is not known, are also condsidered.

Impact and interest:

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ID Code: 15985
Item Type: QUT Thesis (PhD)
Supervisor: Pettitt, Anthony, Anh, Vo, & Mengersen, Kerrie
Keywords: nonlinear time series models, nonlinear transformations, true noise phase curve, parameter iterative refinement, iterative refinement techniques, regression, time-varying amplitudes, polynomial phase, additive noise, estimation and analysis, estimation and analysis of nonlinear time series models, high signal to noise ratios, low signal to noise ratios, efficient estimations, sequential estimations, demodulatin, highest order parameter, phase coefficients, stastitical analysis, bayesian estimation.
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Department: Faculty of Science
Institution: Queensland University of Technology
Copyright Owner: Copyright Simon Andrew Sando
Deposited On: 03 Dec 2008 03:54
Last Modified: 28 Oct 2011 19:41

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