I noticed that the hot new skill right now seems to be high frequency statistical arbitrage. I think that the interest in statistical arbritrage is very closely related to the fact that the New York Stock Exchange is going over to a hybrid system of electronic trading, and one way of thinking about statistical arbritrage is that what you are doing is programming a computer to do what a human being used to do (i.e. recognize short term patterns and profit from them).
The one curious thing is that wavelets and information theory ought to be useful in doing stat arb, but I haven’t seen any references to either being used. One problem that I’m seeing is that wavelets and information theory assume a continuous field or a regular discrete mesh, and when you are dealing with high frequency data, you are getting irregular inputs, and at that point one finds oneself at the cutting edge of applied mathematics.