I read an interview today with Stephane Coquillaud.
He talked about this idea of formulating a data set of the G5 currencies as a pentahedron. The obvious benefit is the fact that there is more information contained in the data and you'll no longer be testing on marginal price movements of single pairs but rather on the entire major currency spectrum.
He mentioned the other benefit of complexifying the data set from a simple 2 dimensional time series to a 5 dimensional cascade of multiple currency pairs is that the complexity itself reduces the tendency of over fitting parameters in back-tests.
Has anyone here attempted anything like this? I'm having a hard time wrapping my head around the data structure needed for this pentahedron "message" and how to calculate it from a collection of 2 dimensional currency pair time series. In the past, I've built a relative currency strength indicator that took incremental market returns from currency pairs and adjusted the relative strength of each individual currency component of the pair. For example if EUR/USD goes up 2%, then I add 2% to EUR and subtract 2% from USD and factor in the movement from over 24 pairs. However, I don't think this is quite the same thing. Suggestions and insight are wholly welcome!