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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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    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. repec:adr:anecst:y:1986:i:4:p:05 is not listed on IDEAS
    3. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124, October.
    4. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986, October.
    5. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, October.
    6. 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.
    7. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    8. 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.
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