Research output: Thesis › Doctoral Thesis
Research output: Thesis › Doctoral Thesis
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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 -