| Author: | Yuen, Tsz Pang |
| Title: | Graphical models and its estimation in time series analysis |
| Advisors: | Wong, Heung (AMA) Yiu, Ka Fai (AMA) |
| Degree: | M.Phil. |
| Year: | 2018 |
| Subject: | Hong Kong Polytechnic University -- Dissertations Graphical modeling (Statistics) Multivariate analysis -- Graphic methods Time-series analysis |
| Department: | Department of Applied Mathematics |
| Pages: | xxiv, 118 pages : color illustrations |
| Language: | English |
| Abstract: | Graphical time series models encode the dynamic relationships among the variables in multivariate time series in graphs, in which nodes represent the variables and edges characterize the conditional dependence. In applications, the graph structure is not known in advance, and it is of interest to estimate and determine the graph based on samples. To determine graphical time series models, we propose two estimation methods based on sparse vector autoregressive models. An alternating maximization method is introduced to estimate sparse vector autoregressive models under sparsity constraints on both the autoregressive coefficients and the inverse noise covariance matrix. This alternating method estimates sparse vector autoregressive models by considering the maximum likelihood estimation with the sparsity constraints as a biconcave problem. Such optimization problem is concave when either the autoregressive coefficients or the inverse covariance matrix is fixed. Simulation experiments study the estimation performance of the alternating method and compare with other non-linear optimization methods. We also introduce two approaches in determining the sparsity constraints. These two methods are studied by simulation studies for comparisons. Real data examples are provided as illustrations. The sparsity constraints in the alternating maximization method, however, require being identified before the estimation procedure. A penalized likelihood estimation for vector autoregressive models is proposed to encourage sparsity on both the autoregressive coefficients and the inverse noise covariance matrix. This penalization method implements penalty terms on the autoregressive coefficients and the off-diagonal elements of the inverse covariance matrix to achieve parsimonious models. The finite sample properties of the penalized likelihood estimator are investigated by simulation experiments. A real dataset application is presented for demonstration. |
| Rights: | All rights reserved |
| Access: | open access |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 991022179237703411.pdf | For All Users | 1.4 MB | Adobe PDF | View/Open |
Copyright Undertaking
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item:
https://theses.lib.polyu.edu.hk/handle/200/9794