Covariation of curves
W. Bauer
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
David Reilly
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
W. Bauer
> 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 ....
Yes, I observe at each point of time the whole curve. But the points where
the jumps are change over time. Does this pose a problem for the "pooled
cross-sectional time series" methodology?
Thanks for the hint, W. Bauer
David Reilly
No ... Because the assumption is that there are N GROUPS or N SEPARATE
AND DISTINCT REGIMES and each regime has t observed contiguous values
( not necessarily equal for all groups ) ..
regards
Dave Reilly
Automatic Forecasting Systems
http://www.autobox.com