ARMA Signals With Specified Symmetric Marginal Probability Distribution

Except in the case of normal (i.e., Gaussian) distribution, it is very difficult to calculate the marginal probability distribution of ARMA signals. By using a particular form of modeling such signals with random coefficients we show that the problem can be solved and we present an algorithm allowing the numerical generation of ARMA signals with arbitrary specified marginal distribution function. Their properties are analyzed in computer experiments. The experimental results show in general a very good agreement with theoretical calculations.