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The spectral analysis of nonstationary categorical time series using local spectral envelope

Jeong, Hyewook and Jeong, Hyewook (2012) The spectral analysis of nonstationary categorical time series using local spectral envelope. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Most classical methods for the spectral analysis are based on the assumption that the time
series is stationary. However, many time series in practical problems shows nonstationary
behaviors. The data from some fields are huge and have variance and spectrum which changes
over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time
series such as EEG sleep state data or DNA sequence, the general method is to scale the
data, that is, assign numerical values to the categories and then use the periodogram to find
the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the
numerical values to the categories and proceed with a spectral analysis, then the results will
depend on the particular assignment. We would like to find the all possible scaling that
bring out all of the interesting features in the data. To overcome these problems, there have
been many approaches in the spectral analysis.
Our goal is to develop a statistical methodology for analyzing nonstationary categorical
time series in the frequency domain. In this dissertation, the spectral envelope methodology
is introduced for spectral analysis of categorical time series. This provides the general
framework for the spectral analysis of the categorical time series and summarizes information
from the spectrum matrix. To apply this method to nonstationary process, I used the
TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise
stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation)
using distance function based on the Kullback-Leibler divergence was proposed to find the
best segmentation.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairStoffer, David/Sstoffer@pitt.eduSTOFFER
Committee MemberChen, Yuyucheng@pitt.eduYUCHENG
Committee MemberMazumdar, Satimaz1@pitt.eduMAZ1
Committee MemberKrafty, Robert/Tkrafty@pitt.eduKRAFTY
Date: 27 September 2012
Date Type: Publication
Defense Date: 6 August 2012
Approval Date: 27 September 2012
Submission Date: 7 August 2012
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 53
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: spectral analysis, spectral envelope, Kullback-Leibler divergence
Date Deposited: 27 Sep 2012 22:48
Last Modified: 15 Nov 2016 14:01


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