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

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