Generating an autocorrelated sequence of random variates without distorting their distribution

Using moving averages to introduce autocorrelation into a sequence of pseudorandom variables will most often distort the shape of the distribution. When the correlation coefficients are to be zero from some lag onward, it is possible to compensate for most of the distortion by starting with variates from another distribution. It is shown how to calculate the moving average coefficients and the parameters of the basic sequence so as to achieve the desired autocorrelation while retaining fidelity with the desired distribution to four moments. The moving average approach yields an internal generation method having quite modest storage requirements.