I agree about the selectivity of data sets, and it's a hard one to call.
For instance Fourier analysis is a perfectly respectable math technique, but is insanely useless to use on interpreting a yield curve.
However, that does give me an idea for a valid bit of research, based loosely upon the the Hearsay/Blackboard AI artchitecture.
A system that actually does the searching through huge volumes of data, recognising ones it can do useful things with, and rejecting those it does not handle, would have value.
A big problem with neural nets, genetic algorithms et al, is that it is hard to trust them when you don't know what their limits are. To me intelligence, or even competence in an area must include the ability to say "I have no idea what this crap is, I'm not getting involved."
But like a lot of people I find myself drawn to AI in finance, indeed I tried to push this many years ago, and learned a really quite impressive set of negative things. As in "X1 does not work, X2, does not work, X3 does not work..."
At the risk of sounding like a buzzword generator I think a thesis of the form
Signal processing in high frequency markets using techniques from electronics, econometrics, and CS. (using C++ of course)
As I said recently in different QN thread, this is currently the most valuable collection of skills you might plausibly have.
But...
Whenever I give advice on PhDs I am exposing you to a big risk.
I have a reasonably good model of what is desired by employers,
at this time, and of course what they have wanted in the past. If I was so smart I could predict the markets in 5 years time I would be doing very different things with my time
Signal processing is quite hot, and
C++ is easily the dominant language.
But...
Two years ago, 95% of entry level quant jobs were
C++ and/or VBA
That's dropped to the high 80s.
C# has grown big time and we expect this year that over 1% of quant jobs will ask for Java, and Java has now overtaken both Smalltalk and Fortran.
SP was extremely rate 3 years ago, and will never be the mass market, and my partner Paul Wilmott is always happy to share the fact that new cool techniques come and go, but PDEs are forever.
Ultimately, I would counsel you to honestly work out where you are better than other people.
A really good neural nets person will do better than a mediocrity in time series analysis.
From that set identify those things that you think will be demanded from banks.