Marco, thank you for sharing this, very interesting. I also got curious about your P.S. - about estimating complexity based on compression rates. It reminded me something we do often in Wolfram Science Summer School. As a research approach we frequently explore space of algorithms and simple programs that produce complex behavior trying to access that complexity with some compression routines. By the way Mathematica has its own Compress function, which also can be used for those purposes. An example fo such project could be:
Exploring CA Rule Spaces by Means of Data Compression
I realized you do research in complex systems and thought this maybe of interest to you or your students. You, your colleagues or students maybe also interested to learn that applications are now open for the 2014 Wolfram Science Summer School. It is a very fun and educational experience I would recommend as a frommer student and a current faculty member there. Also perhaps of interest to you is a post I wrote aboute a mapping between time series and networks - so called Visibility Graphs . This gives some extra graph-theoretical tools to explore complexity of time series.