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Given

  • a time series $T_0$,
  • group 1 of time series $T_{1,1},...,T_{1,n_1}$
  • group 2 of time series $T_{2,1},...,T_{2,n_2}$,
  • ...
  • group m of time series $T_{m,1},...,T_{m,n_m}$,

what are some ways to address the following questions:

  • is $T_0$ more cross-correlated to the series in group 1 than to the series in group 2?

  • To which group among the m groups is $T_0$ most cross-correlated to?

My thought is that

  1. Firstly, calculate the cross-correlation $\rho_{i,j}$ between $T_0$, and $T_{i,j}, i =1,...,m, j=1,...,n_i$
  2. Secondly, for each $i$, calculate the mean of $|\rho_{i,j}|, j=1,...,n_i$ (taking absolute value because cross-correlation can be positive or negative). Compare the means over $i=1,...,m$.
  3. Thirdly, test if the mean of $|\rho_{i_1,j}|, j=1,...,n_{i_1}$ is greater than $|\rho_{i_2,j}|, j=1,...,n_{i_2}$.

    • But what is the right test, given the values here are all nonnegative (because of the absolute values)?
    • But the test is just between two groups $i_1$ and $i_2$, and how can we find the group to which $T_0$ is most cross-correlated to, by testing?
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    $\begingroup$ This idea is perhaps silly, but maybe it will at least serve as an inspiration. What if you just put it all into one regression model (with $T_0$ as the dependent variable) and then compute partial correlation coefficients for the various groups? $\endgroup$
    – hejseb
    Nov 3, 2015 at 6:04

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