FUNCTIONAL CENTRAL LIMIT THEOREMS FOR MULTIVARIATE LINEAR PROCESSES GENERATED BY DEPENDENT RANDOM VECTORS

Title & Authors
FUNCTIONAL CENTRAL LIMIT THEOREMS FOR MULTIVARIATE LINEAR PROCESSES GENERATED BY DEPENDENT RANDOM VECTORS
Ko, Mi-Hwa;

Abstract
Let $\small{\mathbb{X}_t}$ be an m-dimensional linear process defined by $\small{\mathbb{X}_t=\sum{_{j=0}^\infty}\;A_j\;\mathbb{Z}_{t-j}}$, t = 1, 2, $\small{\ldots}$, where $\small{\mathbb{Z}_t}$ is a sequence of m-dimensional random vectors with mean 0 : $\small{m\times1}$ and positive definite covariance matrix $\small{\Gamma:m{\times}m}$ and $\small{\{A_j\}}$ is a sequence of coefficient matrices. In this paper we give sufficient conditions so that $\small{\sum{_{t=1}^{[ns]}\mathbb{X}_t}$ (properly normalized) converges weakly to Wiener measure if the corresponding result for $\small{\sum{_{t=1}^{[ns]}\mathbb{Z}_t}$ is true.
Keywords
functional central limit theorem;Linear process;moving average process;negatively associated;martingale difference;
Language
English
Cited by
1.
A Central Limit Theorem for the Linear Process in a Hilbert Space under Negative Association,;

Communications for Statistical Applications and Methods, 2009. vol.16. 4, pp.687-696
1.
A Central Limit Theorem for the Linear Process in a Hilbert Space under Negative Association, Communications for Statistical Applications and Methods, 2009, 16, 4, 687
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