[QuantEcon]MATLAB混编FORTRAN语言

$$
w_{it} = \alpha_i + \sum_j \gamma_{ij} \ln p_{jt}
   + \beta_i \ln \left( m_t / P_t \right) + u_{it}
$$
Given the fact that the observed budget shares always sum-up to one
$(\sum_i w_{it} = 1 \; \forall \, t)$,

$$
\begin{array}{l}
{x_{1,t}} = {x_{1,t - 1}} + \sigma_1{u_{1,t}}\\
{x_{2,t}} = \phi {x_{2,t - 1}} + \sigma_2{u_{2,t}}\\
{y_t} = {x_{1,t}} + {x_{2,t}}
\end{array}
$$

$$
\begin{array}{l}
{\phi_{z,t}} = {\phi_{z,t - 1}}\\
{x_{2,z,t}} = {x_{2,z,t - 1}} \phi_{z,t}  + 0.8{u_{2,t}}\\
\end{array}
$$

$$
f(x) = \frac{sin(x)}{x}
$$

$$
\sum(x-a)^n \frac{f^{(n )}(a)}{n!}
$$

$$
\left(\begin{array}{c}
-\frac{b+\sqrt{b^2 -4\,a\,c}}{2\,a}\\
-\frac{b-\sqrt{b^2 -4\,a\,c}}{2\,a}
\end{array}\right)
$$

$$
m\,\frac{\partial^2 }{\partial t^2 }\;x\left(t\right)+c\,\frac{\partial }{\partial t}\;x\left(t\right)+k\,x\left(t\right)=F\left(t\right)
$$

$$
m\,\frac{\partial^2 }{\partial t^2 }\;x\left(t\right)+\gamma \,m\,\frac{\partial }{\partial t}\;x\left(t\right)+m\,x\left(t\right)\,{\omega_0 }^2 =F\left(t\right)
$$

$$
\begin{array}{l}
{\left(\frac{{\mathrm{e}}^{-\sigma_1 } }{2}+\frac{{\mathrm{e}}^{\sigma_1 } }{2}-\frac{\gamma \,{\mathrm{e}}^{-\sigma_1 } }{2\,\sqrt{\gamma^2 -4\,{\omega_0 }^2 }}+\frac{\gamma \,{\mathrm{e}}^{\sigma_1 } }{2\,\sqrt{\gamma^2 -4\,{\omega_0 }^2 }}\right)}\,{\mathrm{e}}^{-\frac{\gamma \,t}{2}} \\
\mathrm{}\\
\textrm{where}\\
\mathrm{}\\
\;\;\sigma_1 =\frac{t\,\sqrt{\gamma^2 -4\,{\omega_0 }^2 }}{2}
\end{array}
$$

$$
\left(\begin{array}{c}
\frac{\partial }{\partial t}\;\theta \left(t\right)=\theta_t \left(t\right)\\
\frac{\partial }{\partial t}\;\theta_t \left(t\right)=-{\omega_0 }^2 \,\mathrm{sin}\left(\theta \left(t\right)\right)
\end{array}\right)
$$

$$
\begin{array}{l}
\left(\begin{array}{c}
-\frac{6\,{\left(3\,{x_1 }^2 -1\right)}\,{\left(-{x_1 }^3 +x_1 +x_2 \right)}-2\,x_1 +\frac{8}{3}}{\sigma_1 }\\
\frac{-6\,{x_1 }^3 +6\,x_1 +6\,x_2 }{\sigma_1 }
\end{array}\right)\\
\mathrm{}\\
\textrm{where}\\
\mathrm{}\\
\;\;\sigma_1 ={{\left(x_1 -\frac{4}{3}\right)}}^2 +3\,{{\left(-{x_1 }^3 +x_1 +x_2 \right)}}^2 +1
\end{array}
$$