Uniform random parameter generation of stable minimum-phase real ARMA (p, q) processes

An algorithm to randomly generate the parameters of stable invertible autoregressive moving average processes of order (p, q)-ARMA (p, q)-is presented. The AR and MA portions are independent of each other, and their respective parameters have jointly uniform distributions with support defined by stability and invertibility considerations. The uniform density insures that each possible model is equally likely. The algorithm uses the Levinson-Durbin recursion to guarantee the poles and zeros are inside the unit circle, thus avoiding coefficient resampling typical of "generate and test" methods. To initialize the Levinson-Durbin recursion for each model order, the reflection coefficients are generated using a rejection sampling technique.