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Some topics on time series analysis
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Title
Some topics on time series analysis
Name
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Liu
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Chuan
NamePart
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1987-
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Chuan Liu
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author
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Xiao
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Han
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Han Xiao
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Advisory Committee
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chair
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Rutgers University
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degree grantor
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School of Graduate Studies
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theses
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ETD doctoral
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2020
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2020-10
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2020
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English
Abstract
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This thesis deals with three problems. The first problem is concerned with the classical white noise test, and the second is on the estimation of autoregressive models for matrix-valued time series. These two time series problems are treated in Chapter 2 and 3. The third problem, on the construction of exact algorithm for the linear constrained LASSO, is treated in Chapter 4.
In Chapter 2, we study the asymptotic distribution of sample canonical correlations under different distributional assumptions of the time series. The joint density of the asymptotic distribution is derived explicitly for the normal and elliptical distributions. For the general non-normal case, we propose to bootstrap the canonical correlations to obtain the p-value. We carry out an extensive simulation study to illustrate the size and power performances of the proposed tests.
In Chapter 3, we propose a novel estimator of the matrix autoregressive model, based on the weighted least squares. We derive the asymptotic distributions of the estimator, and demonstrate its performance by simulations and real examples.
Chapter 4 deals with the exact algorithm of the constrained LASSO problem. We develop such an exact algorithm by exploring the geometric properties of the problem. We prove that the solution path of the problem is piece-wise linear. We also prove an exponential upper bound for the complexity of the constrained LASSO problem.
In Chapter 2, we study the asymptotic distribution of sample canonical correlations under different distributional assumptions of the time series. The joint density of the asymptotic distribution is derived explicitly for the normal and elliptical distributions. For the general non-normal case, we propose to bootstrap the canonical correlations to obtain the p-value. We carry out an extensive simulation study to illustrate the size and power performances of the proposed tests.
In Chapter 3, we propose a novel estimator of the matrix autoregressive model, based on the weighted least squares. We derive the asymptotic distributions of the estimator, and demonstrate its performance by simulations and real examples.
Chapter 4 deals with the exact algorithm of the constrained LASSO problem. We develop such an exact algorithm by exploring the geometric properties of the problem. We prove that the solution path of the problem is piece-wise linear. We also prove an exponential upper bound for the complexity of the constrained LASSO problem.
Subject
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Topic
White noise test
Subject
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Topic
Statistics and Biostatistics
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Rutgers University Electronic Theses and Dissertations
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ETD_11209
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1 online resource (xiv, 110 pages) : illustrations
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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doi:10.7282/t3-0c1j-7n68
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The author owns the copyright to this work.
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Liu
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Chuan
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2020-09-28 09:49:51
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Chuan Liu
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Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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Copyright protected
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Open
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Permission or license
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