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On Linear Processes With Given Moments

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  • Jiří Anděl

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.

Suggested Citation

  • Jiří Anděl, 1987. "On Linear Processes With Given Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 373-378, July.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:4:p:373-378
    DOI: 10.1111/j.1467-9892.1987.tb00001.x
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