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

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.

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Are the time series both stationnary ? www.econ.ohio-state.edu/dejong/note1.pdf –  user603 Oct 10 '10 at 11:54
@kwak: No, the series are both NOT stationary. –  morpheous Oct 12 '10 at 17:49
Here: stats.stackexchange.com/questions/1881/… I was proposing a Monte Carlo approach to determine confidence limits. The idea was to do this for two point processes, but I guess it could be easily adapted for your situation. –  nico Oct 13 '10 at 10:53

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...)

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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.

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Other posters have noted that stationarity is important here. If both series have a linear upwards trend (one kind of nonstationarity), they will be correlated - but all the correlation may be due to the common trend, which may or may not be what we are interested in. –  Stephan Kolassa Oct 21 '10 at 13:06