Cross-Covariance ? A laymans explanation?

Question

Following up on this question on the difference between covariance and correlation, how would you explain cross-covariance to a layman?

If possible without formulae.

Answer 1

The intuition should be the same for cross-covariance and cross-correlation, as the later one is just a unit-free version of the former (as explained in the linked post).

The concept of cross-correlation occurs with time series data, we are comparing one variable at one time with another variable at another time point, typically lagged before or after. Lagged signifies that we compare, say, $A_t$ with $B_{t-1}$ where $t$ is the time index. This is called lead/lag relationships, and there are many posts on this site, some is Using lead-lag relationships for time series prediction, Lead-and-lag test?.

Some people hope to use this as market indicators, if the price of one commodity reacts rapidly to some change, and others reacts more slowly, they hope to use the former as an indicator and then help for speculating in the later. Cross-correlations is one of the tools to detect this. There is ALOT of information on the internet ... hope this can give some intuition.