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I am looking to get a better understanding of an output from a trading strategy. Basically I have a daily equity curve lets call it $Y_t$. I have defined a bunch of independent variables $X_{it}$ that I think can explain the movement in the daily PnL. The independent variables are not used in trading signal generation directly.

1) How can I go about deducing which independent variables explain my $Y_t$ , assuming that the relationship could be non-linear? I can start out with PCA but from what I understand it assumes a linear relationship.

2) Using a reduced independent variable set $X_{it}$ from 1) how do I go about defining a non-linear relationship with $Y_t$ . Neural Nets maybe?

I understand that doing 1) and 2) might result in overfitting but I just want to understand the equity curve better.

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The problem with Principle component analysis is that you moght lose information about what really drives your returns. Also as a rule of thumbs, before assuming that you have a non linear relationship make sure that a linear methods realy results in underfitting your problem. If you want to reduce the number of variables you could use shrinkage regression for example. – Zarbouzou Jul 5 '12 at 8:22
I agree with @Zarbouzou, is there any particular reason you are so focused on non-linear relationships? What's wrong with PCA? – Tal Fishman Jul 5 '12 at 17:04
This is really just a generic attribution problem (see papers.ssrn.com/sol3/papers.cfm?abstract_id=1565134 for guidance on how to do that, but there's a large literature on other techniques). The biggest problem is that your holdings will not necessarily be constant over time. So in some periods you may be 100% long pork bellies and others you're 100% short the Sri Lankan rupee. The approach by Meucci I mention above can help with point in time attribution. – John Jul 5 '12 at 21:44

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