Final answer:
Cross-lag correlations can establish temporal precedence and covariation but are not helpful for establishing nonspuriousness because they do not control for confounding variables, potentially leading to a false cause fallacy.
Step-by-step explanation:
Cross-lag correlations help researchers understand the direction and strength of relationships between variables across time. However, they are not helpful for addressing the rule of causation concerning nonspuriousness. This rule requires eliminating alternative explanations for the observed correlation, such as confounding variables, to establish a cause-and-effect relationship. Cross-lag correlations can establish temporal precedence and covariation but do not control for confounding variables, which is necessary to establish nonspuriousness.
It is critical to remember that correlation does not equal causation, and without controlling for all possible confounding variables, it is possible to incorrectly attribute a causal relationship where none exists. This is known as the false cause fallacy or assuming a causation simply because two variables are correlated without sufficient evidence to do so.