[R] comparing predicted sequence A'(t) to observed sequence A(t)

[Suresh Krishna]

Hi,

I have a question that I have not been succesful in finding a definitive 
answer to; and I was hoping someone here could give me some pointers to 
the right place in the literature.

A. We have 4 sets of data, A(t), B(t), C(t), and D(t). Each of these 
consists of a series of counts obtained in sequential time-intervals: so 
  for example, A(t) would be something like:

Count A(t):  25,    28,    26,   34   ......
Time (ms):  0-10, 10-20, 20-30, 30-40 .......

Each count in the series A(t) is obtained by summing the total number of 
observed counts over multiple (say 50), independent repetitions of that 
time-series. These counts are generally known to be Poisson distributed, 
and the 4 processes A(t), B(t), C(t) and D(t) are independent of each other.

B. It appears on visual observation that the following relationship 
holds; and such a relationship would also be expected on mechanistic 
considerations.

A(t) = B(t) + C(t) - D(t)

We now want to test this hypothesis statistically.

Because successive counts in the sequence are likely to be correlated, 
isnt it true that none of these methods are valid ? Perhaps for other 
reasons as well ?

a)Doing a chi-squared test to see if the predicted curve for A(t) 
deviates significantly from the observed A(t); this also seems to not 
take the variability of the predicted curve into account.

b)Doing a regression of the predicted values of A(t) against the actual 
values of A(t) and checking for deviations of slope from 1 and intercept 
from 0 ? Here, in addition to lack of independence, the fact that 
X-values are not fixed (i.e. are variable) and the fact that X and Y are 
Poisson distributed counts should also be taken into account, right ?

I would be very grateful if someone could point me to methods to handle 
this kind of situation, or where to look for them. Is there something in 
the time-series literature, for instance ?

Thanks !!

Suresh