On central limit theorem for a stationary multivariate linear process generated by linearly positive quadrant dependent random vectors (Q2785260)

The author provides a central limit theorem for an \(m\)-variate linear process generated by an \(m\)-variate linearly positive quadrant dependent (LPQD) sequence of random variables. Let \(\{ \mathbf{X}_{t}, t=0,\pm 1, \cdots \}\) be an \(m\)-variate linear process of the form \(\mathbf{X}_{t}=\sum^{\infty}_{u=0}A_{u}\mathbf{Z}_{t-u}\) defined on a probability space \((\Omega,\mathcal{F}, P)\), where \(\mathbf{Z}_{t}\) is a sequence of stationary \(m\)-variate LPQD random vectors with \(E\mathbf{Z}_{t}=0, E\|\mathbf{Z}_{t}\|^{2}<\infty\) and positive definite covariance matrix \(\Gamma_{m\times m}.\) The author proves that a central limit theorem for the multivariate linear process \(\mathbf {X}_{t}\) holds.