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Yule’s “nonsense correlation” for Gaussian random walks

Author

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

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.

Suggested Citation

  • Ernst, Philip A. & Huang, Dongzhou & Viens, Frederi G., 2023. "Yule’s “nonsense correlation” for Gaussian random walks," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 423-455.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:423-455
    DOI: 10.1016/j.spa.2023.04.007
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    References listed on IDEAS

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    4. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124, November.
    5. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    6. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986, November.
    7. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, November.
    Full references (including those not matched with items on IDEAS)

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