Topological Data Analysis and theoretical statistical inference for time series dependent data and error in parametric choices

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dc.contributor.advisorEnsor, Katherine
dc.creatorAguilar, Alex
dc.date.accessioned2022-09-23T21:28:41Z
dc.date.available2023-08-01T05:01:14Z
dc.date.created2022-08
dc.date.issued2022-07-14
dc.date.submittedAugust 2022
dc.date.updated2022-09-23T21:28:41Z
dc.description.abstractTopological data analysis extracts topological features by examining the shape of the data through persistent homology to produce topological summaries, such as the persistence landscape. While the persistence landscape makes it easier to conduct statistical analysis, the Strong Law of Large Numbers and a Central Limit Theorem for the persistence landscape applies to independent and identically distributed copies of a random variable. Therefore, we developed a Strong Law of Large Numbers and a Central Limit Theorem for the persistence landscape when the stochastic component of our series is driven by an autoregressive process of order one. Theoretical results for the persistence landscape are demonstrated computationally and applied to financial time series.
dc.embargo.terms2023-08-01
dc.format.mimetypeapplication/pdf
dc.identifier.citationAguilar, Alex. "Topological Data Analysis and theoretical statistical inference for time series dependent data and error in parametric choices." (2022) Diss., Rice University. <a href="https://hdl.handle.net/1911/113333">https://hdl.handle.net/1911/113333</a>.
dc.identifier.urihttps://hdl.handle.net/1911/113333
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectTopological Data Analysis
dc.subjectDependent Data
dc.subjectAutoregressive Processes
dc.titleTopological Data Analysis and theoretical statistical inference for time series dependent data and error in parametric choices
dc.typeThesis
dc.type.materialText
thesis.degree.departmentStatistics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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