Ye, Cong
(2016)
Multiple Change-point Detection for piecewise stationary categorical time series.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In this dissertation, we propose a fast yet consistent method for segmenting a piecewise stationary categorical-valued time series, with a finite unknown number of change-points in its autocovariance structure. To avoid loss of information, instead of arbitrarily assigning numerical numbers in analysis of the original time series, we focus on the multinomial process, which is derived by denoting each category of the original series as a unit vector. The corresponding multinomial process is then modeled by a nonparametric multivariate locally stationary wavelet process, where the piecewise constant autocovariance structure for any given variate is completely described by the wavelet periodograms for that variate at multiple scales and locations. Further, we propose a criterion that optimally selects the scalings and provides the generation of the trace statistics whose mean functions inherit the piecewise constancy. The resulting statistics will serve as input sequences for later segmentation. Change-point detection is accomplished by first examining the input sequence at each scale with the binary segmentation procedure, and then combining the detected breakpoints across scales. The consistency result of our method is established under certain conditions. In addition, several simulation studies and a real-data analysis of a DNA sequence are provided to demonstrate the viability of our methodology.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
22 January 2016 |
| Date Type: |
Publication |
| Defense Date: |
18 November 2015 |
| Approval Date: |
22 January 2016 |
| Submission Date: |
24 November 2015 |
| Access Restriction: |
1 year -- Restrict access to University of Pittsburgh for a period of 1 year. |
| Number of Pages: |
63 |
| 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: |
categorical-valued time series, piecewise stationarity, locally stationary wavelet process, wavelet analysis, binary segmentation, DNA sequences. |
| Date Deposited: |
22 Jan 2016 19:34 |
| Last Modified: |
22 Jan 2017 06:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/26469 |
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