How do I generate a random process value given a set of moments or cumulants?

How would a create a data set from a known set of data moments or cumulants.

Its fairly easy to generate a random number with a known variance and mean. I would like to get something that lets me submit an array of cumulants (or moments)

Example: (ci = cumulent, mi = momemts)
  c1 = m1 or ‘mean’
  c2 = m2 − m1 = σ2 or ‘variance’ (σ = standard deviation)
  c3 = m3 − 3*m1*m2 + 2*m3 or ‘skewness’
  c4 = m4 − 3*m2 − 4*m1*m3 + 12*m1*m2 − 6*m1 or ‘kurtosis' 

So I would like a function, f, that takes a bunch of ci values and produces a single data point whose array of historical values maintains the specified cumulants.

 y(i) = f(c1,c2,c3,..., and optionally [y(i-1), y(i-2), ...])

See Moments, Cumulants and Scaling