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

  • 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.

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Author:Uwe HasslerORCiDGND, Mehdi Hosseinkouchack
Parent Title (English):Statistical papers
Place of publication:Berlin ; Heidelberg [u.a.]
Document Type:Article
Date of Publication (online):2021/05/06
Date of first Publication:2021/05/06
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/10/20
Tag:Coin tossing; Concordance; Discordance; Maximum length of association
Page Number:15
First Page:181
Last Page:195
Open Access funding enabled and organized by Projekt DEAL.
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - Namensnennung 4.0