Yule’s “nonsense correlation” for Gaussian random walks

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

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 423-455

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.

Keywords: Nonsense correlation; Gaussian random walks; Wiener processes; Wasserstein distance (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.04.007

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