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.

考虑两个独立的随机游动。偶然地，在两个过程朝着相同方向或相反方向移动的过程中，它们之间会出现关联咒语。对于给定的样本量，我们计算了这种随机关联的最长咒语长度的概率，并讨论了精确分布的均值和众数之类的度量。我们观察到，随机关联的长咒语（相对于小样本量）经常发生，这解释了为什么短独立随机游走之间的无意义关联是规则而不是例外。将精确数字与近似值进行比较。我们的有限样本分析及其近似值依赖于Révész推广的两个较早的结果（Stat Pap 31：95-101，1990，Statistics Papers）。此外，我们考虑了相关随机游走之间的关联咒语。将近似概率与有限样本蒙特卡洛结果进行比较。