Covariation of curves

Dear all

Instead of real valued random variables, I would like to analyze step 
functions. I observe a time series for each of N step functions. These step 
functions are monotonically increasing and have finite many steps. If it 
helps the analysis, a continuous approximation would also be fine. I would 
like to study whether the covariation of the curves is driven by some 
factors, i.e. whether the variation in the shape of the curves has common 
components.

The only methodology dealing with statistics of curves that I've found so
far is Small and McLeish: Hilbert space methods in probability and
statistical inference. Yet, the seem to study "univariate" curves, not
families of "curve valued random variables".

Any suggestion as on an appropriate statistical model is very much 
appreciated,

W. Bauer