I am a total newbie when it comes to time series, so it is quite possible this question is duplicated somewhere else, only that I cannot find it because I don't know what this feature is called.
I have weekly measurements of a variable "change in rank". I also have weekly measurements of another variable loosely described as "change in goodness". I believe that "change in rank" is dependent on "change in goodness", but I also believe that whenever "goodness" improves, it takes some time before rank improves. A simplistic representation of the data would look like this:
change_in_rank = c(0,0,0,0,-10,0,0,0) change_in_goodness = c(0,2,0,0,0,0,0,0)
where this constructed example shows that a improvement of 2 in goodness took 3 time steps to lead to an improvement in rank.
What analysis method do I use to detect whether such a relationship actually exists between "change in goodness" and "change in rank", and if such a relationship exists, how do I find out how long it takes for a change in "goodness" to flow on to a change in rank.
The motivation behind this question:
Some additional, non necessary background: it is claimed that search engine optimisation takes time to affect your site's ranking in Google. E.g.:
I am trying to find a statistical way of calculating how long it takes for a change in a site to actually reflect in the site's Google ranking.
Slightly different type of data but similar question...