PCA is an incredibly useful technique. At work we've been using it to model the structure of the yield curve, i.e. the graph of interest rates vs. maturity. Turns out you can decompose most daily movements of the yield curve into three components: parallel shift up/down, steepening/flattening, and a "bow" where 2s5s flattens, 5s10s steepens, and 10s30s flattens.. It would be interesting to build an interest rate model that evolves these three components forward in time... it would probably be most useful for short time scales where the principal components are unlikely to change.
unrelated question: I've been recently been reading a lot about wavelets and multiscale analysis. My application area is in text processing and topic models for legal document analysis. Wavelet transforms or statistical modeling in the wavelet domain seems like the kind of thing that would have been tried many times over in finance. Do you know of any instances when it turns out to be useful useful for time series?
I've heard people talk about it, but never seen any concrete applications to finance. If you know of any papers or introductory material, I'd be thrilled to check it out. I know nothing about wavelets or multiscale analysis -- I couldn't even define them if you asked -- but I have a decent math and statistics background so I'd love to take a look.
