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
- Firstly, calculate the cross-correlation $\rho_{i,j}$ between $T_0$, and $T_{i,j}, i =1,...,m, j=1,...,n_i$
- 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 $i=1,...,m$.
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?