DislikedThe asymmetry also bothered me as well. The following paper showed an approach based on PCA which eliminates the asymmetry of the 'reference'.
http://www.scribd.com/doc/23407376/R...Multi-VarianceIgnored
Could I just take this opportunity to thank you very much for posting this link to the OU paper. Finally over Christmas I have had chance to sit down quietly and read it. It has been a long time since I read such an interesting paper. So many pennies dropped reading this!! Several sets of scales have fallen from my tired old eyes!
If you look at the "standard" econometrics literature (where no-one has a clue about linear algebra), they bang on at huge length about the differences between MA and AR processes, how to combine them into ARMA, endless tests for distinguishing trend-stationary from difference-stationary series, endless variations on the Augmented Dickey Fuller tests where you can get any answer you want by fiddling with the parameters! Blah blah blah ad nauseam!
The OU framework presented in the article is brilliant. It is so straightforward once it is laid out in simple terms. Once you have projected the data into the eigenspace of its own covariance, everything else follows from standard control theory and state-space analysis that any engineer will be familiar with. We are on safe and familiar ground at last!
We can now dispense with all the various unit root tests etc etc and distinguish exactly what sort of animal we are dealing with simply from the partitioning of the eigenspace. We can separate the stationary and co-integrated parts (and note carefully from the paper that these are NOT interchangable!) from the non-stationary parts. We should now be able to build baskets with rigorously provable finite variance and a significant chance of profitability with quantified risk control.
Very nice indeed. Thanks once again for your valuable contribution. Posts like that one make FF the diamond mine it sometimes is. OK, you have to shovel through tons and tons of crap, but now and again you find a real sparkler!
Very best regards,
Old Dog