I have a data of two time series variables. Both of them have trend.
I want to test whether the two variables are correlated.
what is the appropriate correlation measure for such type of data?
Hi,
I think that you need to analyse the cross correlations between the series (this show the correlation at different lags) . These statistics assume that the time series are stationary.
There are at least two possibilities:
1. the trends are correlated
and/or
2. the deviations from the trends are correlated.
Obviously, an appropriate test in the case of correlated trends require careful setting of the model. A first idea to follow is to devide both series into the trend and the perturbating parts; and then perform standard correlation procedure of the trends and separately of the perturbations.
Hopefully, it helps.
Regards, Joachim
dear prof. Joachim Domsta
can you please explain what is perturbations and how to perform it
@ Srikanth Potharla
Dear Sir, I expected this question. More covenient for me but obviously not polite would be to return with a question: and what is the trend? But one can easily guess that this is the average. Thus, to be more concrete: If the sequence of observations of one of the series - say ...,x(-1),x0,x1,x2,. . . has a trend which you are detecting by some averaging procedure, e.g. by moving arithmetic mean
xavk = (x(k-L) + x(k-L+1) + . . . x(k+L) )/ (2L+1)
then I will call the differences xk - xavk , k=... -2,-1,0,1,2,3,... a pertubation process and the averages xavk a trend process. Next you can analyse the two processes for the x-coordinates and the corresponding two for the y-coordinates separately: in particular you can analyse the correlation between xavk and yavk as the core of the process of your interest, and between xk - xavk and yk - yavk as some noise processes, which should be uncorrelated.
All above has associated to me due to your formulation. My imagination worked toward tohe question - what is the role of the trend. My answer is biased by the meaning, that you are interested in seeking the dependence of the core values of y on the core values of x. If this is not he case then, please, forget my ad hoc found algorityhm.
Regards, Joachim Domsta
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