... and it's something that perhaps we don't look at quite often enough!
What am I talking about? Well, let's imagine that we're interested in the relationship between two signals, , and . One of the most basic analyses we might do is ask "are they correlated?" But perhaps the correlation depends on the timescale that we focus on. Could a signal be positively correlated at once timescale and negatively correlated at another scale?
Since I've shown you an example, hopefully you believe that a signal could be positively correlated at one timescale and negatively correlated at another! Here, and are positively correlated on a long timescale but negatively correlated on a short timescale.
Can we characterize this sort of relationship? Yes, and I'll outline one way of characterizing this sort of time-scale dependent correlation below.