Multivariate Nonstationary Time Series: Spectrum Analysis and Dimension Reduction

This dissertation tackles two important problems in modern multivariate nonstationary time series analysis: spectrum analysis and dimension reduction. The first part of the dissertation introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood based penalized spline models of modified Cholesky components, which provide flexible nonparametric estimates that preserve positive definite structures of spectral matrices. The approach is formulated in a Bayesian framework, in which the number and location of partitions are random, and relies on reversible jump Markov chain and Hamiltonian Monte Carlo methods that can adapt to the unknown number of segments and parameters. The second part of the dissertation aims to shed lights on the usefulness of contemporaneous aggregation for high--dimensional time series analysis, especially in the forecasting point of view. Compared to other computationally intensive methods, contemporaneous aggregation has several advantages: it is simple and easy to use, it is much more computationally efficient, and its forecasting properties are well-known. We propose a statistical measure to quantify the advantages of using contemporaneous aggregation, and provide general guidelines to researchers on when to use contemporaneous aggregation.

Grantor dc:publisher

Temple University. Libraries

Year dc:date.issued

2018

Author dc:creator

• Li, Zeda

Advisors dc:contributor.advisor

• Wei, William W. S.
• Krafty, Robert T.

Committee members dc:contributor.committeemember

• Dong, Yuexiao
• Zhao, Zhigen
• Chervoneva, Inna

• Statistics

Statement dc:rights

• IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/20.500.12613/3196

OAI identifier oai:identifier

oai:scholarshare.temple.edu:20.500.12613/3196