ica and quantitative finance

this site has some interesting papers on quantitative finance. in particular, i think the report on quant education would be an interesting read, even though it is a bit old now. the other paper, 'a first application of independent component analysis to extracting structure from stock returns' is the earliest reference i've seen on ica on financial data. now a number of people have been doing it, with mixed results imho. but there is a good point to be made here in that, if you are assuming independence, why just look at correlation? why choose an orthogonal basis orientation based on reprojection error L_2 minimization? why not look at mutual infomation or higher order moments and cumulants? if there are components that are uninterpretable, it is self-deceptive to force them to be small artificially and it will probably lead to overly optimistic estimates of risk. truth is, i have two goals for modeling log price relative time series: classification and time-windowed average estimation. for classification i want independence, and for the time averages i want to minimize time-averaged error (not necessarily time-averaged error^2). not only is amplitude significant; autocorrelation of the error time series is, too.