| Abstract: | Abstract. Let X t = c 0 Y t + c 1 Y t -1+… be a linear process with known coefficients c k , where Y t is a strict white noise. Let m 1, …, m 2r be given numbers. A method is presented to determine whether there exists a distribution of Y t such that EX k t = m k for k = 1, …, 2 r . In the positive case, such a distribution of Y t is described. Some explicit formulas for AR(1) and AR(2) models are derived. The results can be used for simulating a process with given moments of its stationary distribution. The procedure also enables proof that some stationary distributions cannot belong to the given linear process. |
