How to visualise observations of a stochastic process with a parameter change? I've obtained 2840 observations of a stochastic process with large Gaussian noise. The process parameters change at one point around the 1500th observation. I've ensemble-averaged these into sets of 10, 40 and 284 observations and would like to present those three sets to the readers of my report, but I can't figure out a good way of visualising this data.
Ideally, the visualisation would let the viewer see:


*

*the wave morphology

*the impact of noise, i.e. how much one averaging differs from another in the set

*the point where the wave morphology changes


I could plot them all in a single graph. This gives a good idea about the impact of noise, but loses the chronological order of the waves. Also, it would only work for the set of 10 before becoming unmanageable.

I could also plot them as a 3D surface with the X axis showing time in a sample and the Z axis the ordinal number of the observation. One problem is that some waves are seen better than others, making it hard to compare the noise levels and wave morphologies quantitatively from the graph.

How could I best visualise these averaged sets of observations?
 A: If you're sure that it changes at one point, you can do two plots: one for the prebreak realizations and one for the postbreak realizations.  If you're not sure  that it only changes at a point, you can break things up into smaller subsets and look at them all separately.  Here's some illustrative R code that uses the lattice package and conditions on blocks of the time period:
library(lattice)
rprocess <- function(n, slope) {
  x <- slope * (1:n) + rnorm(n)
  cbind(i = 1:n,
        x = (4/n) * (1:n) * sin(10 * (1:n) / n) + x)
}

nFns <- 200
obsPerFn <- 200
d <- data.frame(do.call(rbind, 
  c(lapply(1:nFns, function(t) 
           cbind(t = t, rprocess(obsPerFn, 0))),
    lapply(nFns + (1:nFns), function(t) 
           cbind(t = t, rprocess(obsPerFn, -.2))))))

xyplot(x ~ i | (t - 1) %/% 45, groups = t, type = "l",
       data = d, col = rgb(0,0,0,.3), layout = c(9, 1))

Obviously it could be improved a lot.
If you can plot the data before averaging, you probably want to do that as well -- you'd like to use the graphics to complement your model/analysis and to convince the readers that it's appropriate, and that's much less compelling if only processed data are presented.
