| dc.identifier.uri | http://hdl.handle.net/11401/76338 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | Change-point stands for the times of discontinuities in a time series that can be induced from changes in distribution. Change-points widely exist in the time series data in the real world, such as the field of climate and finance. A bunch of models have been developed for change-point detection, however, not many of them focus on the covariance matrix. In this dissertation research, the goal is to find a model to detect change-points of covariance matrix. The difficulties originally come from the dimensionality. In multiple dimensional space, covariance matrix acts as the same role as that of variance in one dimensional space. However, situation gets more complicated as dimension getting higher. Much more noise exists in multiple dimensional space than that in one dimensional space. We expect the model is capable to filter the noise as much as possible, in the meanwhile, it reserves enough information for parameter change. Besides, we have to search a good tool to measure the change of a matrix, which is not as simple as that in one dimensional space. In this dissertation, motivated by the spirit of principal component analysis (PCA), we propose the eigen-structure to measure the change of matrix. PCA will be briefly reviewed in the first chapter. The model used for detecting change-point is proposed by Lai and Xing (2011). The model is a Bayesian model relies on an assumption of exponential family resulting in a closed form for the final estimated parameter. We also present the derivation of explicit formulas for a special case: the data is normally distributed, for both one and multiple dimensional cases. The explicit formulas contributes to the simplicity of the Bayes model. For the purpose of improving calculation speed, BCMIX, an approximated algorithm, as well as several algorithms for eigen-decomposition are introduced in the beginning of the simulation part. The results of simulation will be shown afterward. At last, the model is applied to several real data sets with satisfactory results obtained. | |
| dcterms.available | 2017-09-20T16:50:03Z | |
| dcterms.contributor | Zhu, Wei | en_US |
| dcterms.contributor | Xing, Haipeng | en_US |
| dcterms.contributor | Wu, Song | en_US |
| dcterms.contributor | Xu, Jinfeng. | en_US |
| dcterms.creator | Song, Yuzhou | |
| dcterms.dateAccepted | 2017-09-20T16:50:03Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:03Z | |
| dcterms.description | Department of Applied Mathematics and Statistics. | en_US |
| dcterms.extent | 110 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76338 | |
| dcterms.issued | 2015-08-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:03Z (GMT). No. of bitstreams: 1
Song_grad.sunysb_0771E_11736.pdf: 1561710 bytes, checksum: 256c1de5379dec481931140cf8be1b35 (MD5)
Previous issue date: 2014 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Statistics | |
| dcterms.title | Structure Breaks in PCA with Applications in Finance | |
| dcterms.type | Dissertation | |
