Cross correlation and t tests

#1
I have two time series data from two machines arranged sequentially ( machine 1 output goes is machine 2 input) . I wanted to compare the mean utlisation of these machines and see which one is higher over a given period of time. The
two time series data is cross correlated.
. So my question is which t test I should use ? Paired t test or independent t test? As I am not comparing the measurements on the same subject is it ok to use independent t test .?

Note : t test is corrected for auto correlation in the time series data using wilks approach..
 
#2
It's all correlated, between the machines and over time. So neither a t-test nor a Wilcoxon test is appropriate. You should model the tasks as counting processes where the intensities are deterministic or stochastic functions of time. The models can be estimated via the method of maximum likelihood. Then you can compare the intensities over each sub-interval of interest.