I would probably do the circshift function and search for the highest correlation. But if the first minimum works wells then stick with that.
Remember when you circshift that the values loop around so the the beginning of your time series (however many steps you shifted by) is not longer valid and should be removed from the analysis.
Here's a simple example of what I'm suggesting
series1=cos(0:.1:8*pi())';
series2=sin(0:.1:8*pi())';
plot(series2,'r')
hold on
plot(series1)
for t=1:64 % 64 is one period length
cm=corrcoef(series2,circshift(series1,t));
c(t)=cm(1,2);
end
[~,I] = max(c); % I is best value for circshift
