Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2016
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Anant Godbole, Michele Joyner, Nicole Lewis
Abstract
The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens theorem approach to make the manifold reconstruction outcomes of Takens theorem less sensitive to noise. In particular, in the course of performing the SSA on a noisy time series, we branch of into a Takens theorem approach. We apply this approach to a variety of noisy time series.
Document Type
Dissertation - unrestricted
Recommended Citation
Torku, Thomas K., "Takens Theorem with Singular Spectrum Analysis Applied to Noisy Time Series" (2016). Electronic Theses and Dissertations. Paper 3013. https://dc.etsu.edu/etd/3013
Copyright
Copyright by the authors.
Included in
Algebra Commons, Applied Mathematics Commons, Longitudinal Data Analysis and Time Series Commons, Other Statistics and Probability Commons, Statistical Models Commons