# How to better understand trading signals?

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.

-

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
– John Jul 5 '12 at 21:44
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9439505338668823, "perplexity_flag": "middle"}