− | x_{t+1}=Ax_t+\varepsilon_t, A\in\mathcal{R}^{n\times n}, \varepsilon_t\sim\mathcal{N}(0,\Sigma), ${\rm rk}(A)={\rm rk}(\Sigma)=n | + | x_{t+1}=Ax_t+\varepsilon_t, A\in\mathcal{R}^{n\times n}, \varepsilon_t\sim\mathcal{N}(0,\Sigma), {\rm rk}(A)={\rm rk}(\Sigma)=n |
− | y_{t+1}=A_M y_t+\varepsilon_{M,t}, $A_M=WAW^\dagger\in \mathcal{R}^{k\times k}$, $\varepsilon_{M,t}\sim \mathcal{N}(0,\Sigma_M), \Sigma_M=W\Sigma W^{T}$. $W^\dagger$ | + | y_{t+1}=A_M y_t+\varepsilon_{M,t}, A_M=WAW^\dagger\in \mathcal{R}^{k\times k}, \varepsilon_{M,t}\sim \mathcal{N}(0,\Sigma_M), \Sigma_M=W\Sigma W^{T} |