thank you maysam for your response

You can use cross-correlation. It reminds convolution, but it more suitable to 'real-data' graphs. make sure that you use implementation that reduce the base line (the average) and divides by the Std to be able to interpret the results

Dear Ariel

thanks a lot and good luck

It depends. Are the periods iqual? If the time series has some similar trend, then its better to remove the trend at first. Are the time series stationary? Did you make an unit root test? I think it is appropriate to make also a co-integration test, in case they are not stationary.

Alternatively, Can you assume that each pairwise pointset contains random members, then demonstrate that they are not statistically random? That behavior should lead you to an appropriate model.

Dear Celso

thank you for your answer, time series are not periodic, actually we extracted some complex time series

Dear Todd

thanks a lot, which model do you mean? I didn't get your mean correctly

Dear Julien

thank you so much for your response

good luck