On a central limit theorem for a stationary multivariate linear process generated by linearly positive quadrant dependent random vectors

摘要

For a stationary multivariate linear process of the form $ mathbb{X}_{t}= {displaystylesum_{j=0}^infty} A_j mathbb{Z}_{t-j}$, where ${ mathbb{Z}_t : t=0, pm1, pm2, cdots }$ is a sequence of stationary linearly positive quadrant dependent $m$-dimensional random vectors with $E(mathbb{Z}_t)= mathbb{O}$ and $E|mathbb{Z}_t |^2 < infty$, we prove a central limit theorem.