|Title:||Modelling nonlinear dynamics of time series with applications|
|Subject:||Hong Kong Polytechnic University -- Dissertations.|
|Department:||Department of Electronic and Information Engineering|
|Pages:||xx, 127 leaves : ill. ; 31 cm.|
|Abstract:||Nature, as human beings observe it, brings forth rich and colorful phenomena which are recorded as time series. We usually wish to understand the underlying dynamics hidden under these time series. An efficient way of capturing dynamics is by time series modelling. As it became obvious that nonlinear dynamics abounds in the world, nonlinear modelling techniques were greatly studied and developed. This thesis describes building optimal nonlinear models based on an information theoretic criterion to investigate the underlying dynamics of various time series, especially cardiovascular time series (electrocardiograph and pulse data). The purpose of this research is to determine whether these techniques may be used to extend our understanding of the human cardiovascular system. We wish to build the relationship between the EGG and pulse data, and then classify distinct dynamics from recording of cardiac data. The major problem endemic to either linear or nonlinear models with a large number of parameters is overfitting. The usual methods of avoiding this problem are to avoid fitting the data too precisely, but these techniques can not determine the exact model size directly. We propose an alternative, information theoretic criterion to determine the optimal models. When applied to time series prediction these optimal models both generalize well and accurately capture the underlying nonlinear dynamics. The preceding optimal modelling techniques have been employed to model blood pressure propagation from the human wrist to the fingertip. We apply the well-known surrogate data method to model residuals, and conclude that there is no significant difference between pulse waveforms measured on the lateral artery (wrist) and fingertip. We then investigate the deterministic dynamics of EGG and pulse data, and the relationship between them. The surrogate data method against the null hypothesis of linear noise, does not provide sufficient evidence to confirm the existence of deterministic dynamics in them. We present a recently suggested pseudo-periodic surrogate method to determine whether they are consistent with deterministic chaos. Algorithmic complexity is proposed as the robust test statistic of the surrogate data method. Short-term prediction from EGG to pulse data and vice versa by our optimal models are also described. The results indicate that bounded aperiodic determinism exists in both EGG and pulse data. We conclude that the human EGG data contains information of the human body that pulse data does not have or can not replicate. The feasibility and utility of complexity and the surrogate data method for identification of nonlinear dynamics in noisy experimental data is also studied in this thesis. To provide an additional independent test system we apply these techniques to the international effort to experimentally observed gravitational waves. We propose complexity to detect the simulated gravitational data contaminated with strong noise. Complexity is proved to be robust and very sensitive to the existence of gravitational waves. The surrogate data method is used to examine the deterministic dynamics in the noisy gravitational data and attach statistical significance to the results estimated by complexity.|
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