Re: Statistical test for equality ?

[pathematica]

I apologise if the following is known to you and does not apply to your
model. However, you have possibly opened a different can of worms there. 

Stock prices comprise time series, whose data cannot be modelled by
processes that assume independence of successive variables because each term
in the series cannot be considered independent of the others (classic
example from textbooks: the temperature on one day will almost certainly
depend in some way on that of the day before in a country that is located in
a temperate zone because of the effects of seasons; in general, temperatures
in summer are likely to be higher than those in winter). Techniques exist to
raise equations that mimic the variation in some already recorded time
series, so that the observed data and the simulated data (which requires a
seed) raise graphs that look similar through the period of observation in
which the data were recorded. Such curves work well in interpolation but
they are notoriously bad at extrapolation (that is at predicting future
trends). I realise that speculators nevertheless invest large resources in
attempting to raise models that will be used to predict future stock prices,
and the rewards of a successful model are potentially enormous. 

Simulated curves used in interpolation (and extrapolation at the user's
risk) are often a composite of two techniques: one that smooths data
(typically a moving average) to remove variation modelled as noise; and one
that attempts to capture cyclic variation (typically autoregression) eg of
the type described for temperature across seasons. I expect that you will
know that combined models of this type are called ARIMA ones (autoregression
integrated moving average). 

As noted, I apologise if all of that is known to you. It might provide
avenues for further research if it is not. 



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