Generating pseudo-random time series with specified marginal distributions

Our goal is to generate a target time series with a specified marginal distribution and a specified lag-one autocorrelation. We consider an existing approach: first transform a known autocorrelated reference series into the corresponding uniform autocorrelated series and then apply the specified inverse transformation to each observation producing the target series. This approach is simple, except that the lag-one reference-series autocorrelation must be determined in a set-up step. We propose a method for determining this autocorrelation.