Permutation-based inference in time series analysis

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Permutation testing is a widely used tool for performing robust and nonparametric inference in a variety of settings. Given observations from a stationary time series, permutation tests allow one to construct exactly level alpha tests under the null hypothesis of an independent and identically distributed (i.i.d.) or, more generally, exchangeable distribution. However, in a general time series setting, the null hypothesis permits distributions which are not i.i.d., in which case permutation tests are not necessarily level alpha, nor are they approximately level alpha in large samples. In this thesis, we present a general framework for restoring the validity of the permutation testing procedure in large samples in a time series context, while retaining the exact rejection probability alpha in finite samples when the observations are i.i.d. Under weak assumptions on the mixing coefficients and moments of the sequence, we show that appropriate studentization of the test statistic leads to asymptotically valid inference in a permutation testing context. In particular, we describe explicitly the permutation testing procedure for three problem applications: testing for dependence in time series, permutation tests based on ordinary least squares regression, and permutation testing for detection of monotone trend.


Type of resource text
Form electronic resource; remote; computer; online resource
Extent 1 online resource.
Place California
Place [Stanford, California]
Publisher [Stanford University]
Copyright date 2023; ©2023
Publication date 2023; 2023
Issuance monographic
Language English


Author Tirlea, Marius Aurel
Degree supervisor Romano, Joseph P, 1960-
Thesis advisor Romano, Joseph P, 1960-
Thesis advisor Duchi, John
Thesis advisor Owen, Art B
Degree committee member Duchi, John
Degree committee member Owen, Art B
Associated with Stanford University, School of Humanities and Sciences
Associated with Stanford University, Department of Statistics


Genre Theses
Genre Text

Bibliographic information

Statement of responsibility Marius Tirlea.
Note Submitted to the Department of Statistics.
Thesis Thesis Ph.D. Stanford University 2023.

Access conditions

© 2023 by Marius Aurel Tirlea
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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