discrete signals - How do I know quantitatively if the correlation of two time series is significant?

I computed the correlation coefficient of two time series of daily observations, x and y, but noticed that the more sampling points I used in the calculation, the lower the value of the correlation coefficient, until it reaches saturation at very long time.

It looks that the correlation coefficient is related to the number of points and it's unable to set a fixed threshold to the correlation coefficient. So, how can I know quantitatively if the correlation is significant?

Answer

p-value and t-test look to be solutions.

There is no other answer up to now. I keep this simple answer and shall remove if we have other good ones.