Computing correlation (and the significance of said correlation) between a pair of time series

Question

I have two time series S, and T. they have the same frequency and the same length.

I would like to calculate (using R), the correlation between this pair (i.e. S and T), and also be able to calculate the significance of the correlation), so I can determine whether the correlation is due to chance or not.

I would like to do this in R, and am looking for pointers/skeletal framework to get me started.

Answer 1

How do you define correlation for non stationary time series? Do you plan to take the correlation of the diff or these time series? If not, I suggest you look for cointegration rather than correlation (cf Granger etc...)

Answer 2

You can use the ccf function to get the cross-correlation, but this will only give you a plot. If the estimated cross correlations fall outside the dash red line, then you can conclude that there is a statistically significant cross-correlation. But I do not know of a package with a formally encapsulated test. Example from ccf doc:

require(graphics)

## Example from Venables & Ripley (Provided in  CCF help file)
ccf(mdeaths, fdeaths, ylab = "cross-correlation")

Note, that the question of significance test is also discussed here.