statisticaly significant difference between two time series data

I have two sets of time series data(series1 and series2). Each dataset has 20 samples for 20 time intervals (one sample per each time interval). I want to see if these two datasets are significantly different. What test should I use? More precicely, I am trying to predict the population of people for 20 time intervals. I have used two different methods to make this prediction that is why I have two sets of data. I want to see which prediction is better and more accurate. I also have the real numbers of population to evaluate my prediction. I have calculated the RMSE for the two series of prediction. The mean RMSE for series2 is less than series1but I am not sure if it is a sufficient criteria to say that series2 is better prediction than series1.