TY  - JOUR
A1  - Hassler, Uwe
A1  - Hosseinkouchack, Mehdi
T1  - Understanding nonsense correlation between (independent) random walks in finite samples
T2  - Statistical papers
N2  - 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.
KW  - Coin tossing
KW  - Concordance
KW  - Discordance
KW  - Maximum length of association
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63722
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-637223
SN  - 1613-9798
N1  - Open Access funding enabled and organized by Projekt DEAL.
VL  - 63
IS  - 1
SP  - 181
EP  - 195
PB  - Springer
CY  - Berlin ; Heidelberg [u.a.]
ER  -