I am not familiar with the concept of entropy for time series. I am looking for good reference papers and examples of use.
Answer
As a good starting point read this recent paper by Jing Chen:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1734526
For a special use of the entropy concept for forecasting the '87-crash read this paper:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=959547
(Although I tried to contact the authors to get the data to reproduce their findings, which they didn't send, it is still an enlightening read)
For a more popular exposition of the use of entropy in money management (key word 'Kelly formula') you should read this intelligent page turner by Poundstone: Fortunes Formula
EDIT: Quite an interesting paper is this one where Black-Scholes is derived through the use of concepts of relative entropy: http://www.mdpi.com/1099-4300/2/2/70/
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