State space models Consider the model $$ T_t = T_{t-1} + \epsilon_t $$ $$ S_t = 0.8S_{t-4} + \eta_t $$ $$ Y_t = T_t + S_t + V_t $$ where $(\epsilon_t) \sim WN(0,\sigma_1^2)$, $\eta_t \sim WN(0,\sigma_2^2)$, and $(V_t) \sim WN(0,\sigma_3^2)$. We observe data $Y_1,\ldots,Y_n$. Write the model in the standard (matrix) form of a linear Gaussian state space model