Yule’s “nonsense correlation” for Gaussian random walks
File(s)
Published version
Author(s)
Ernst, Philip A
Huang, Dongzhou
Viens, Frederi G
Type
Journal Article
Abstract
This paper provides an exact formula for the second moment of the empirical correlation (also known as Yule’s “nonsense correlation”) for two independent standard Gaussian random walks, as well as implicit formulas for higher moments. We also establish rates of convergence of the empirical correlation of two independent standard Gaussian random walks to the empirical correlation of two independent Wiener processes.
Date Issued
2023-08
Date Acceptance
2023-04-08
Citation
Stochastic Processes and their Applications, 2023, 162, pp.423-455
ISSN
0304-4149
Publisher
Elsevier BV
Start Page
423
End Page
455
Journal / Book Title
Stochastic Processes and their Applications
Volume
162
Copyright Statement
© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC
BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Identifier
http://dx.doi.org/10.1016/j.spa.2023.04.007
Publication Status
Published
Date Publish Online
2023-04-26