Yule’s “nonsense correlation” for Gaussian random walks

Ernst, Philip A.; Huang, Dongzhou; Viens, Frederi G.

Yule’s “nonsense correlation” for Gaussian random walks

Files

1-s2-0-S0304414923000753-main.pdf (1.65 MB)

Date

2023

Authors

Ernst, Philip A.

Huang, Dongzhou

Viens, Frederi G.

Publisher

Elsevier

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.

Type

Journal article

Citation

Ernst, Philip A., Huang, Dongzhou and Viens, Frederi G.. "Yule’s “nonsense correlation” for Gaussian random walks." Stochastic Processes and their Applications, 162, (2023) Elsevier: 423-455. https://doi.org/10.1016/j.spa.2023.04.007.

Published Version

https://doi.org/10.1016/j.spa.2023.04.007

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