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  • 2014ParkPhD

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Wavelet Methods for Multivariate Nonstationary Time Series

Research output: ThesisDoctoral Thesis

  • Timothy Alexander Park
Publication date2014
Number of pages156
Awarding Institution
  • Lancaster University
<mark>Original language</mark>English


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 locally
stationary 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.