Testing correlation with overlapping data

I have 3 initial time series: Dividends (D), Earnings(E) and Yields (Y). Further I need to compute the moving sums of dividends and earnings, so that

D_new(t)=sum(D(t-11):D(t)).

So the variable D_new and E_new becomes overlapping with 11 lags. Y remains non-overlapping. Could you please me help me with testing the significance of correlation coefficient, because traditional t-test will give wrong estimates as I understand. Consider 3 cases: 1) Correl(D_new(t),E_new(t)) 2) Correl(D_new(t), Y(t)) 3) Correl(D_new(t), D_new(t-1)). Please find the file with data example attached for better understanding. Thanks a lot!