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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 27, Fasc. 2,
pages 235 - 245
 

SOME REMARKS ON THE CENTRAL LIMIT THEOREM FOR FUNCTIONALS OF LINEAR PROCESSES UNDER SHORT-RANGE DEPENDENCE

Konrad Furmańczyk

Abstract: In this paper we consider the central limit theorems for functionals $G: \mathbb (R)^m1 \to \mathbb (R)$ of one-sided $m$-dimensional linear processes $X_t = \sum _(r=0)^\infty A_r Z_(t-r)$, where $A$ is a nonrandom matrix $m \times m$ and $Z_r$’s are i.i.d. random vectors in $R^m$.

2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary: 60G10.

Key words and phrases: Central limit theorem, linear process, time series, short-range dependence, Markov chain, martingale differences.

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