AR(1) processes with given moments of marginal distribution. (English) Zbl 0701.62087

Summary: Let \(X_ t\) be an AR(1) process given by \(X_ t=bX_{t-1}+e_ t\) where \(b\in (-1,1)\) and \(e_ t\) is a strict white noise. Sometimes \(X_ t\) must satisfy also some additional conditions, e.g. \(X_ t\geq 0\) or \(C\leq X_ t\leq D\). The problem solved in the paper is how to find a distribution of \(e_ t\) such that the moments E \(X_ t^ k\) \((k=1,...,n)\) have given values.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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