Correlation between two time series What is the easiest way / method to compute the correlation between two time series that are exactly the same size? I thought of multiplying $(x[t]-\mu_x)$ and $(y[t] - \mu_y)$, and adding up the multiplication. So if this single number was positive, can we say these two series are correlated? I can think of some examples however where a linearly another exponentially growing time series would have no relation to eachother, but the computation above would report they were correlated. 
Any thoughts?
 A: You might want to look at a similar question and my answer Correlating volume timeseries which suggests that you can compute cross-correlations BUT testing them is a horse of a different color ( an equine of a different hue ) due to autoregressive or deterministic structure within either series.
A: Macro's point is correct the proper way to compare for relationships between time series is by the cross-correlation function (assuming stationarity).  Having the same length is not essential.  The cross correlation at lag 0 just computes a correlation like doing the Pearson correlation estimate pairing the data at the identical time points.  If they do have the same length as you are assuming, you will have exact T pairs where T is the number of time points for each series. Lag 1 cross correlation matches time t from series 1 with time t+1 in series 2.  Note that here even though the series are the same length you only have T-2 pair as one point in the first series has no match in the second and one other point in the second series will not have a match from the first.  Given these two series you can estimate the cross-correlation at several lags .  If any of the cross correlations is statistically significantly different from 0 it will indicate a correlation between the two series.
A: There is some interesting stuff here
https://stackoverflow.com/questions/3949226/calculating-pearson-correlation-and-significance-in-python
This was actually what I needed. Simple to implement and explain. 
