A central limit theorem for the stationary multivariate linear process generated by associated random vectors

Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 95-102 Printed March 1, 2002

Tae-Sung Kim, Mi-Hwa Ko, and Sung-Mo Chung WonKwang University, WonKwang University, WonKwang University

Abstract : A central limit theorem is obtained for a stationary multivariate linear process of the form $\mathbb{X}_{t} = \sum_{u=0}^\infty A_u \mathbb{Z}_{t-u}$, where $\{\mathbb{Z}_t \}$ is a sequence of strictly stationary $m$-dimensional associated random vectors with ${E \mathbb{Z}_t = \mathbb{O}}$ and $E\|\mathbb{Z}_t \|^2 < \infty$ and $\{A_u \}$ is a sequence of coefficient matrices with $\sum_{u=0}^\infty \|A_u \| < \infty$ and $\sum_{u=0}^\infty A_u \not= O_{m \times m}$.

Keywords : central limit theorem, stationary, multivariate linear process, associated random vector