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New models and methods for time series analysis in big data era

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TitleInfo
Title
New models and methods for time series analysis in big data era
Name (type = personal)
NamePart (type = family)
Liu
NamePart (type = given)
Xialu
NamePart (type = date)
1986-
DisplayForm
Xialu Liu
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Chen
NamePart (type = given)
Rong
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Rong Chen
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Xiao
NamePart (type = given)
Han
DisplayForm
Han Xiao
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Dicker
NamePart (type = given)
Lee
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Lee Dicker
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Lin
NamePart (type = given)
Xiaodong
DisplayForm
Xiaodong Lin
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2015
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2015-05
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2015
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
In big data era, available information becomes massive and complex and is often observed over time. Conventional time series models are limited in capability of dealing with these type of data. This dissertation focuses on developing new statistical models, along with their associated estimation procedures, to analyze time series data in functional form, and in high dimension, with linear or nonlinear dynamics, which can be broadly applicable to finance, environment, engineering, biological and medical sciences. Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who worst introduced the functional autoregressive (FAR) models, we propose a convolutional functional autoregressive (CFAR) model, where the function at time t is a result of the sum of convolutions of the past functions with a set of convolution functions, plus a noise process, mimicking the autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. We adopt a sieve estimation procedure based on the B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. As for high-dimensional time series data, dimension reduction is an important issue and can be effectively performed by factor analysis. Considering the factor impacts may vary under different conditions, we propose a factor model with regime-switching mechanism, allowing loadings to change across regimes, and combined eigendecomposition and Viterbi algorithm for estimation. We discover that, with multiple states of different 'strength', the convergence rate of loading matrix estimator for strong states is the same as the one-regime case, while the rate improves for weak states, gaining extra information from strong states. The theoretical properties of the procedure are investigated as well. In addition, we propose a new class of nonparametric seasonal time series models under the framework of the functional coefficient model. The coefficients in the proposed model change over time and consist of the trend and seasonal components to characterize seasonality. A local linear approach is developed to estimate the nonparametric trend and seasonal effect functions. The proposed methodologies are illustrated by two simulated examples and the model is applied to characterizing the seasonality of the monthly number of tourists visiting Hawaii.
Subject (authority = RUETD)
Topic
Statistics and Biostatistics
Subject (authority = ETD-LCSH)
Topic
Time-series analysis
Subject (authority = ETD-LCSH)
Topic
Big data
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_6327
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (xiii, 124 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Xialu Liu
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3WQ05MJ
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Liu
GivenName
Xialu
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-04-13 10:51:28
AssociatedEntity
Name
Xialu Liu
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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ETD
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windows xp
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