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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.

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