What are some techniques for sampling two correlated random variables:
if their probability distributions are parameterized (e.g., log-normal)
if they have non-parametric distributions.
The data are two time series for which we can compute non-zero correlation coefficients. We wish to simulate these data in the future, assuming the historical correlation and time series CDF is constant.
For case (2), the 1-D analogue would be to construct the CDF and sample from it. So I guess, I could construct a 2-D CDF and do the same thing. However, I wonder if there is a way to come close by using the individual 1-D CDFs and somehow linking the picks.