Principal dynamical componentsQuoteA procedure is proposed for the dimensional reduction of time series. Similarlyto principal components, the procedure seeks a low-dimensional manifold thatminimizes information loss. Unlike principal components, however, the procedureinvolves dynamical considerations, through the proposal of a predictivedynamical model in the reduced manifold. Hence the minimization of the uncertaintyis not only over the choice of a reduced manifold, as in principal components,but also over the parameters of the dynamical model, as in autoregressiveanalysis and principal interaction patterns. Further generalizations are providedto non-autonomous and non-Markovian scenarios, which are then applied to historicalsea-surface temperature data.I though that's something interesting. Do you think it could be applied successfully to implied volatility dynamics or to rate curve term structure dynamics ?

A) Yes: It certainly seems like a useful way to create a compact description of historical implied volatility dynamics or rate curve term structure dynamics.B) No: Yet it would seem less likely that it can create predictions of future dynamics of the implied volatility or rate curve term structure.C) Maybe: The usefulness of any kind of principal components approach would seem to depend on whether: 1) the system is accurately defined by linear mixing of a small number of persistent orthogonal components; 2) the time-variation in the component weights is low WRT the sample window (modeling dynamical components probably helps); 3) the residual effects (all non-dominant modes) are drawn from a non-fat-tailed distribution so they can be safely ignored by practitioners.

PCA could be viewed as P&L volatility reduction tool for any hedging strategy as long as its inherent assumptions do not violate no-arbitrage conditions. From that perspective it becomes a quite useful tool for optimal hedging of linear rates portfolio. Some firms seem to be actively applying it in their swap books.