Re: Covariation of curves

"W. Bauer" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> 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


W.B.

As I understand your statement "I observe a time series for each of N
step functions" ...this means to me that you observe a sequence in
time of real
values for EACH of n steps ....

In effect you can characterize each time series separately and you
wish to test the hypothesis of a common characterization.

If this is true then I would recognize this as a "pooled
cross-sectional time
series problem".

I and others at AFS have been working on schemes to test such
hypotheses and have implemented this feature into our software (
AUTOBOX/FreeFore) . If you would like please send us your data and we
will be happy to analyze it and report the results to the list.

Regards

Dave Reilly
Automatic Forecasting Systems
http://www.autobox.com

P.S. If you wish to talk to me , please call .....215-675-0652