I am interested in quantifying the similarity between 2 time-series. Can I simply sum the squared values of their differences, ie compare the sum of square residuals?

More specifically, I have some observed data that can be represented as a time series. I am able to simulated this data and would like to find the most accurate simulation run.

These simulations are controlled by 2 discrete variables: $-3 <= A <= 3$ and $1 <= B <=10$. The simulations perform reasonably well, but I'd like the find the optimal values of $A$ and $B$ for calibration. I have simulated all 70 possible combinations. Is the above approach sufficient? Or might some other approach be better?

As an additional consideration, I am actually trying to model a multi-variate response, where each response variable is also a time series. Suppose that I would like to simultaneously fit on all of these response variables. Could I sum or average the SumSquaredResiduals to compare to the other simulation combinations?


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I compared each simulation run to the real data. For each dependent variable of interest, I quantified the relationship using mean squared error. To combine these multi-variate MSE's I used Euclidean distance for each simulation run. I then chose the pair of discrete variables A & B that produces the min Euclidean distance of MSEs.


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