Just in case you haven't noticed it, Grant Foster has been writing a series of blog posts about data analysis with AAVSO data. They are very well written and easy to read and follow for someone new to data analysis. His most recent post is about ways of looking for period change in data.
Grant is a former employee of the AAVSO in the 80's and 90's and he occasionally appears at AAVSO meetings where he gives talks on the subject. He designed many of the algorithms still in use today for period analysis in variable star data, such as WWZ and CLEAN. He also wrote the first versions of software the AAVSO gave out for implementing those routines. You can now run the analysis using David Benn's excellent, and free, software called VStar. We have a short tutorial for how to use VStar here.