April 26th, 2007, 2:02 pm
Hi, I have same question as you. Do you have any solution now? I am eager to know your answer soon.Thanks!QuoteOriginally posted by: xyzyangA more challenging question on how to generate correlated random nubmers. From the discussion it is quite simple, at least theoretically, to generate correlated random numbers in N(0,1), Chol would suffice. In my work, we need to generate correlated random numbers that also correlated to a given set of random numbers. For specifically, we have a set of random numbers x1, x2, x3, (say just 3 to make it simple), that could be from history. We can not or do not want to, change them. The question is to find y1, y2, y3, y4 ( 4 is not equal to 3), such as x1, x2, x3, y1, y2, y3, y4 satisfy certain variance-covariance matrix, say, A. Let's analyze it a little more. A must be a 7 by 7 matrix (positive defnite). We also notice that x1, x2, x3 are fixed, we can not generate them any more, so the upper left submatrix (3 by 3) of A is exactly the variance covariance matrix of x1, x2, x3. Then A is decompose into A = (A11, A12; A21, A22). A22 is the variance covariance matrix of y1, y2, y3, y4 while A12 is the correlation matrix of X's and Y's. That is great, so far. Now the problem is: 1. design a algorithm to solve for and simulate y1, y2, y3, y4, prove it theoretically correct 2. practical issue. I have not seen any algorithm or programs that give me truly independent random numbers. not sure if any body has one ---- if you do, please share. 3. as the sizes increase, that is, not 3 or 4, instead, N and M, it quickly become a challenge to see the number of simulations we have to do in order to truly get what we expected Any good ideas?ThanksXYZ