I hope everyone is doing well. I have two time series data sets (Time Series 1) and (Time Series 2). These two series are produced monthly (from 1-2020 to 12-2020) 12 data points. Thus, I took the difference (diff = Time Series 1 - Time Series 2) at each month. I would like to test whether the mean of this difference (diff data set) equals zero - a test that is similar to paired t-test. What is a valid statistical test in this case? I didn't think paired t-test is valid here because it is a time series. I include the plots to illustrate the data set.
Other posts suggested fitting ARIMA model. I don't think it's valid because I only got 12 data points.