I have computed correlation coefficients for 90 day increments of a time series (i.e., one coefficient for days 0-90, 91-180, etc.). It was computationally very expensive to compute these and I would like to analyze correlations over 6 month periods, 1 year periods etc. Is it possible to some how to combine these coefficients? I.e., can I get the correlation over 180 days as 0.5*c1+0.5*c2?
I know in the general case this cannot be done, but because the coefficients are computed from the same number of samples, is it possible?