How to simulate data with same mean, variance and autocorrelation

How to simulate or create a AR(1) process that have the same mean, variance and autocorrelation as the original set of data? Any ideas? Thanks.

Answer 1

[Image Analyst]

You can take the histogram of the original data, then generate random numbers from the cdf of the original histogram. http://en.wikipedia.org/wiki/Inverse_transform_sampling I'm not sure you can get the same autocorrelation though - I'm thinking not.

Answer 2

[Matt J]

Using the known mean and variance, you can determine the 2 parameters of the AR(1) process using the formulas provided here.

Once those 2 parameters are fixed, however, you have no more degrees of freedom with which to independently specify the autocorrelation. However, in case it's useful info, the link also describes the form of the autocovariance and spectral density that you'll be stuck with.