Dear Ivan,

That is an interesting question. While you are right that some times an anticorrelation can be brought about by a time-shifted positive association, the very-low-frequency nature of the BOLD signal fluctuations that we typically look at in resting state analyses makes this interpretation somewhat unlikely for several reasons. First, even if the signal was purely sinusoidal (this is the case where a negative association is exactly the same as a half-period-shifted positive association), band-pass filtered BOLD signal periods range between 10s and 100s, so the phase-shift would need to be between 5s and 50s, which are far from "small phase-shifts" in practical terms. And second, the BOLD signal spectral power is more typically distribued over a the entire range of frequencies within the bandpass filter, and a single time-shift does not unique result in an equivalent phase-shift (phase-shift will be different for each frequency), making it less likely that a time-shifted positively-associated timeseries will result in a net negatively-associated timeseries. In any way, I imagine that ultimately the best approach would be to look at this empirically, for example performing a crosscorrelation analyses of the two timeseries and seeing whether any indication of a non-zero-lagged peak in the correlation appears. Another, perhaps simpler, approach that you could easily do in CONN would be to perform a new first-level analysis using a single seed in the 'sources' list, changing the 'temporal order' field from 0 to 1 (to add first-order temporal derivatives to the model), and using "multivariate regression" or "semipartial correlation" measures. Adding the first-order temporal derivatives to your model allows for some small time-shift correction of the assocation. You can then explore the results for the *_der1 and *_der2 sources separately (the zero-order and first-order derivative terms, respectively) to evalute whether there is any indication of non-zero optimal time-shift in the association (indicated by a non-zero _der2 term) and whether that results in a shifted correlation sign (indicated by a sign-shifted _der1 term) 

Hope this helps
Alfonso

 
Originally posted by Yang Yang: