Statistical test - Time-series - Marketing I want to compare to see if there is a statistically significant difference
between the mean of times-series A and time-series B.
Each time series represent the amount of daily revenue for each campaign. Both campaigns are targeting a different list of users. Each user can be in one of the lists but not in another.
Both time series have lag 1 autocorrelation of  > 0.5, so it seems t-test should not be used here.
Is there a statistical test I can use to compare the means of the groups?
 A: A $t$-test assesses how big the difference in means are relative to the estimation precision. The latter is characterized by the standard error of the mean. In absence of autocorrelation, it is the standard deviation of the sample divided by $\sqrt{n}$ where $n$ is the sample size. In presence of autocorrelation, the usual estimate is biased and invalid. A remedy is to use autocorrelation-robust, or HAC, standard error. It accounts for the bias due to autocorrelation and delivers a valid estimate of precision. This is the only modification needed to make your $t$-test valid.
A: When two campaigns' values follow the same trend through time,  their difference through time should be just noise with no trend; this defined as an ARIMA (0,0,0,0) model.
When we apply ARIMA modeling to Campaign A -Campaign B  we have the best model (using R function auto.arima) is ARIMA(0,0,0,0) with mean 21.0. Hence, we have noise with no trend or autocorrelation close to zero.
Then, we can use the standard T test for the difference  Campaign A -Campaign B; for your dataset we get t = 2.4592, df = 19, p-value = 0.02369 and mean difference is 21.05
When the difference is not white noise, then, mostlikely will change through time.
