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Wavelet Methods for Multivariate Nonstationary Time Series

Research output: Thesis › Doctoral Thesis

Published

Standard

Wavelet Methods for Multivariate Nonstationary Time Series. / Park, Timothy Alexander.
Lancaster University, 2014. 156 p.

Research output: Thesis › Doctoral Thesis

Harvard

Park, TA 2014, 'Wavelet Methods for Multivariate Nonstationary Time Series', PhD, Lancaster University. https://doi.org/10.17635/lancaster/thesis/1389

APA

Park, T. A. (2014). Wavelet Methods for Multivariate Nonstationary Time Series. [Doctoral Thesis, Lancaster University]. Lancaster University. https://doi.org/10.17635/lancaster/thesis/1389

Vancouver

Park TA. Wavelet Methods for Multivariate Nonstationary Time Series. Lancaster University, 2014. 156 p. doi: 10.17635/lancaster/thesis/1389

Author

Park, Timothy Alexander. / Wavelet Methods for Multivariate Nonstationary Time Series. Lancaster University, 2014. 156 p.

Bibtex

@phdthesis{40831386231243a5b4b6dc363c0bd63f,
title = "Wavelet Methods for Multivariate Nonstationary Time Series",
abstract = "This thesis proposes novel methods for the modelling of multivariate time series. The work presented falls into three parts. To begin we introduce a new approach for the modelling of multivariate non-stationary time series. The approach, which is founded on the locally stationary wavelet paradigm, models the second order structure of a multivariate time series with smoothly changing process amplitude. We also define wavelet coherence and partial coherence which quantify the direct and indirect links between components of a multivariate time series. Estimation theory is also developed for this model.The second part of the thesis considers the application of the multivariate locallystationary wavelet framework in a classification setting. Methods for the supervised classification of time series generally aim to assign a series to one class for its entire time span. We instead consider an alternative formulation for multivariate time series where the class membership of a series is permitted to change over time. Our aim therefore changes from classifying the series as a whole to classifying the series at each time point to one of a fixed number of known classes. We also present asymptotic consistency results for this framework.The thesis concludes by introducing a test of coherence between components of a multivariate locally stationary wavelet time series.",
author = "Park, {Timothy Alexander}",
year = "2014",
doi = "10.17635/lancaster/thesis/1389",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - THES

T1 - Wavelet Methods for Multivariate Nonstationary Time Series

AU - Park, Timothy Alexander

PY - 2014

Y1 - 2014

N2 - This thesis proposes novel methods for the modelling of multivariate time series. The work presented falls into three parts. To begin we introduce a new approach for the modelling of multivariate non-stationary time series. The approach, which is founded on the locally stationary wavelet paradigm, models the second order structure of a multivariate time series with smoothly changing process amplitude. We also define wavelet coherence and partial coherence which quantify the direct and indirect links between components of a multivariate time series. Estimation theory is also developed for this model.The second part of the thesis considers the application of the multivariate locallystationary wavelet framework in a classification setting. Methods for the supervised classification of time series generally aim to assign a series to one class for its entire time span. We instead consider an alternative formulation for multivariate time series where the class membership of a series is permitted to change over time. Our aim therefore changes from classifying the series as a whole to classifying the series at each time point to one of a fixed number of known classes. We also present asymptotic consistency results for this framework.The thesis concludes by introducing a test of coherence between components of a multivariate locally stationary wavelet time series.

AB - This thesis proposes novel methods for the modelling of multivariate time series. The work presented falls into three parts. To begin we introduce a new approach for the modelling of multivariate non-stationary time series. The approach, which is founded on the locally stationary wavelet paradigm, models the second order structure of a multivariate time series with smoothly changing process amplitude. We also define wavelet coherence and partial coherence which quantify the direct and indirect links between components of a multivariate time series. Estimation theory is also developed for this model.The second part of the thesis considers the application of the multivariate locallystationary wavelet framework in a classification setting. Methods for the supervised classification of time series generally aim to assign a series to one class for its entire time span. We instead consider an alternative formulation for multivariate time series where the class membership of a series is permitted to change over time. Our aim therefore changes from classifying the series as a whole to classifying the series at each time point to one of a fixed number of known classes. We also present asymptotic consistency results for this framework.The thesis concludes by introducing a test of coherence between components of a multivariate locally stationary wavelet time series.

U2 - 10.17635/lancaster/thesis/1389

DO - 10.17635/lancaster/thesis/1389

M3 - Doctoral Thesis

PB - Lancaster University

ER -