All,Ages since I posted here - hello again to all.I have been playing with PCA, and I like it. But I am unsure how to progress. I have several different swap curves (let's just look at 3), in markets where both the spot and the swap curves are correlated and cointegrated and serially auto- and cross- correlated. You get the idea - it's all the same junk.Now I've taken log returns (not necessarily the best, but OK for now) and have run a PCA analysis on the returns of all maturities of all 3 swap curves, each starting with its appropriate spot.I appear to have come up with very sensible eigenvectors (they seem to represent the expected curve parrallel/skew/bend etc plus some differences between the curve responses) and it seems I can get 99% juice out of just 6 components. So using these 6 eigenvectors, I have produced my factor timeseries.Now comes my problem: These timeseries are clearly full of information and not at all Brownian. They all appear to be mean reverting to zero, and many if not all seem to be cointegrated (some pos, some neg), and I believe there is some autocorrelation too (presumably I should be disturbed to see lagged cross correlations at this point?)... I will test these of course, but let's assume my eyes do not deceive me.So what now? I want to get back to forecasting a change to the curves. So I need to forecast a change to the factors. I expect I should be doing some kind of Vector Auto Regression? But this stuff is so inter-related still, so what's best? Reduced VAR, VECM, or something else? I am not too familiar with either of these yet, so don't blind me! I'm thinking reduced VAR but then how to parameterise? I have read that Bayesian is good, but these are PCA factors, so how can I guess at a prior distribution?Many thanks for any help!

Hi phildrew,You need to find a function that predicts the conditional mean vector and volatility matrix of the multivariate interest series that you have. CCC-GARCH models are widely used, but I would recomend the paper by Audrino and Trojani (2004). But you like PCA, so I will try help. With PCA, however, you are just extracting components that express the variance of the multivariate series. If you want to use these components to predict the future, then you will need to use a multiple output regression methodolgy to predict, one step ahead, for example, these components. Neural Networks, for instance, can be use to model multiple outputs.Your concerns, a) non-normal behavior, agree, but you can use ICA insted of PCA. Nonetheless, Audrino and Trojani methodolgy may help you, since they use a nonparemetric estimation technique. b) auto and cross-correlations, agree, Audrino and Trojani methodolgy may help you.Hope this helps!

your PC's should be orthongonal. have you checked? If you find correlations between PC's you may need to rotate them, google varimax routine.