Consider a system process given by $x_t$=-0.9$x(t-2)$+$z_t$,t=1,2,…,n with observation $y_t$=$x_t$+$v_t$ where {$z_t$} and {$v_t$} are independent white noise with variances $σ^2$ and $σ_v$$^2$. Assume that

$x_0$~N(o,$σ_0$$^2$) and x(-1)~N(0,$σ_1$$^2)$, and that $x_0$ and x(-1) are independent. Write the system and observation equations as state-space model with clearly defined parameters Φ, $A_t$, Q, R, $μ_0$, and $Σ_0$.

Consider a system process given by $x_t=-0.9x_{t-2}+z_t$,$t=1,2,…,n$ with observation $y_t=x_t+v_t$ where ${z_t}$ and ${v_t}$ are independent white noise with variances $σ^2$ and $σ_v^2$. Assume that $x_0\sim \mathcal N(0,σ_0^2)$ and $x_{-1}\sim \mathcal N(0,σ_1^2)$, and that $x_0$ and $x_{-1}$ are independent. Write the system and observation equations as state-space model with clearly defined parameters $\Phi$, $A_t$, $Q$, $R$, $μ_0$, and $Σ_0$.