Ok, though I would advise against the path you're taking right now (for a sanity-check, please post what your top 10 Search terms are right now?).
To finalize your testing criteria, answer the following questions to generate a test list. You must make sure that you have the lists in order to prove a positive first. Get the list from Metrics directly, not the API:
If you're testing against stage, what are the top 10 terms for the certain period that you are selecting?
If you're testing against production, what are the top 10 terms for the certain time period you are selecting?
If you cant generate a list from the metrics console first, there is no way you're going to be able to generate a list from the API. So my advice is to at least establish that there is data there in the Web UI first.
I cant provide you a list of of the request working, because what you're asking for can only be provided if you we are both Admins on the same site. Meaning, I could not give you an example URL of a successful call here on the Lithosphere because you are not an Admin here. Likewise, I am not an Admin on your staging or Production site, so it is difficult to give you an example from your site.
If you are getting an "Access Denied" message, it is one of three things:
1. You are not an Admin
2. You are testing against stage and there is a restriction at the Apache level because of HTaccess
3. You do not have read REST API permissions set for an Admin (very unlikely, but still possible)