Correlation between two time series of very different frequency? I am wondering if there is a limit to calculation of the correlation between two vectors symbolizing events of VERY different frequency.


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*A = events that can appear in the millisecond area

*B = events that appear only several times in 15 minutes.
Does it make sense to correlate such unevenly spaced vectors at all? Is there a ratio of the two occurrences where correlation is impossible? 
 A: Let us show that there can be a correlation, but does not have to be one. 
We turn to cryptography for our examples. If we have a random sequence of digits, the frequency of occurrence of any digit will be unrelated (no surfeit correlation) to the frequency of occurrence of the next digit, or $n^{\text{th}}$ digit thereafter, no matter how large $n$. If we started randomizing two unrelated sequences in binary, and converted one of those to base 1024 by combining ten consecutive binary "digits", there would still be no predictive value for a correlation between the different random sequences, but only because they were unrelated to begin with. Thus, any correlation we would calculate using  self-deceptive methodology would have no predictive value, i.e., there is no meaningful correlation (=0). 
As a counter example, suppose that we take a random binary sequence and compare it to itself in base 1024. Does the correlation decrease because of the change in base? If we calculate correlation so that it is not self-deceptive but is predictive our correlation should be 1 because we are comparing something to itself, even though the sequence itself is perfectly random. If we shift the encoded series by one random binary digit out of 10 ($2^{10}=1024$), before encoding it, the optimal correlation will drop, but not disappear. 
The more relevant question is how to calculate a predictive correlation coefficient in such circumstances. However, the actual question related to the existence of a solution with the answer being that one may exist. With respect to a more general difference in frequency, signal loss from averaging may be a  consideration.
A: You need to come up with a process that generates these correlated events, then you can estimate its parameters. The way you described your data it seems that you imply correlated frequencies. For instance, you could create two series with frequencies which are measured on minute intervals, then look at corsscorrelations
