ON LINEAR PROCESSES WITH GIVEN MOMENTS

Jiří Anděl

Journal of Time Series Analysis, 1987, vol. 8, issue 4, 373-378

Abstract: Abstract. Let Xt=c0Yt+c1Yt‐1+… be a linear process with known coefficients ck, where Yt is a strict white noise. Let m1, …, m2r be given numbers. A method is presented to determine whether there exists a distribution of Yt such that EXkt=mk for k= 1, …, 2r. In the positive case, such a distribution of Yt 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.

Date: 1987
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