$x=f(Y)$ $x$ $Y$ $y_{j,t} = f_j(y_t, y_{t-1}, \ldots, y_{t-k})$ $y_{j,t} = f_j(y_t, y_{t+1}, \ldots, y_{t+k})$ $g_j(y_{j,t}, y_t, y_{t-1}, \ldots, y_{t-k})=0$ $g_j(y_{j,t}, y_t, y_{t+1}, \ldots, y_{t+k})=0$ $g_j(y_{j,t}, y_t, y_{t-1}, \ldots, y_{t-k} ,y_t, y_{t+1}, \ldots, y_{t+k})=0$ $10^{-10}$ $\lambda$ $var(y_{t+k}\vert t)$ $t$ $t-1$ $t+1$ $y_t = y^s + A y^h_{t-1} + B u_t$ $y^s$ $y$ $y^h_t=y_t-y^s$ $y_t = y^s + 0.5 \Delta^2 + A y^h_{t-1} + B u_t + 0.5 C (y^h_{t-1}\otimes y^h_{t-1}) + 0.5 D (u_t \otimes u_t) + E (y^h_{t-1} \otimes u_t)$ $\Delta^2$ $C$ $D$ $E$ $y_t = y^s + G_0 + G_1 z_t + G_2 (z_t \otimes z_t) + G_3 (z_t \otimes z_t \otimes z_t)$ $z_t$ $n_z$ $G_0$ $G_1$ $G_2$ $n_z(n_z+1)/2$ $(i_1, i_2)$ $1$ $i_1 \leq i_2$ $i_1 \neq i_2$ $G_3$ $n_z(n_z+1)(n_z+2)/6$ $(i_1, i_2, i_3)$ $i_1 \leq i_2 \leq i_3$ $i_1 \neq i_2$ $i_1 \neq i_3$ $i_2 \neq i_3$ $(a,a,b)$ $(a,b,a)$ $(b,a,a)$ $\max_\gamma E(y'_tWy_t)$ $A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t-1}+C e_t=0$ $\gamma$ $A_1$ $A_2$ $A_3$ $e$ $y = \left(\alpha^{1/\xi} \ell^{1-1/\xi}+(1-\alpha)^{1/\xi}k^{1-1/\xi}\right)^{\xi/(\xi-1)}$ $= (w \ell)/(p y)$ $\alpha$ $\rho$ $\rho = 0.8, 0.9, 1$