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Understanding nonsense correlation between (independent) random walks in finite samples

Author

Listed:
  • Uwe Hassler

    (Goethe University Frankfurt)

  • Mehdi Hosseinkouchack

    (University of Mannheim)

Abstract

Consider two independent random walks. By chance, there will be spells of association between them where the two processes move in the same direction, or in opposite direction. We compute the probabilities of the length of the longest spell of such random association for a given sample size, and discuss measures like mean and mode of the exact distributions. We observe that long spells (relative to small sample sizes) of random association occur frequently, which explains why nonsense correlation between short independent random walks is the rule rather than the exception. The exact figures are compared with approximations. Our finite sample analysis as well as the approximations rely on two older results popularized by Révész (Stat Pap 31:95–101, 1990, Statistical Papers). Moreover, we consider spells of association between correlated random walks. Approximate probabilities are compared with finite sample Monte Carlo results.

Suggested Citation

  • Uwe Hassler & Mehdi Hosseinkouchack, 2022. "Understanding nonsense correlation between (independent) random walks in finite samples," Statistical Papers, Springer, vol. 63(1), pages 181-195, February.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:1:d:10.1007_s00362-021-01237-0
    DOI: 10.1007/s00362-021-01237-0
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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. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    3. Uwe Hassler, 2003. "Nonsense regressions due to neglected time-varying means," Statistical Papers, Springer, vol. 44(2), pages 169-182, April.
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