Little offtopic highjacking: does it make sense to "bootstrap" correlation among stock returns (frankly, any multidimensional time series, but since we're talking about stocks) with different time periods?

Say, for any pair of stock a and b, randomly selecting a startint point and a period (N days) and using this as a better estimator for the "true" correlation instead of using all the data points? Or something like this, not this process exactly