Correlation with a random walk Correlation with a random walk:
Thanks for kind explanations. But I am still confusing. A random walk repeats previous values plus stochastic fluctuations. Then, can exogenous factors influence a random walk? Exogenous factors may disturb a random walk once, and the random walk will keep the shock permanently, but it will still be a random walk. Unless an exogenous factor causes a trend in a random walk, how can it make the random walk related with another variable that contains a deterministic trend? Is it also possible for a exogenous factor to cause a trend in a rnadom walk? If we consider the population of a random walk, not the one during a limited time of observation, shouldn't there be no relationship with another variable with a deterministic trend? Do I understand something inaccurately here?

Yes, it is – in a sense that the sample correlation will tend to appear statistically significant more often than a nominal significance level suggests it should under the null hypothesis of zero correlation.
