I have two time series, as in the picture below. The data was gathered experimentally. A practical example could be a measured mass flow rate, where I measure the mass flow rate over a certain time period with changing boundary conditions, and I am interested in the total mass of fluid consumed during this period.
The depicted intervals represent the Standard error of the mean and were determined through ten repeated measurements of the entire cycle. For each time step, the interval equals: $ SEM= \frac{\sigma}{\sqrt{10}}$ The ten replications naturally constitute ten identifiable time series.
I now have three questions:
How can I assess, at a specific time step, if the difference between the means of the time series is statistically significant? t-test?
How can I determine the SEM of the cumulated value for each time series?
How can I assess if the difference between the cumulated values of both time series is statistically significant?
Does it make sense to create an "interval" of the cumulative value of both time series by cumulating the upper bound values and lower bound values?