[QuantEcon]MATLAB混编FORTRAN语言

$$
CI_{s} = \sum_{u=u_1}^{^uNC} \sum_{i=i_1}^{^iN} UR_{ui/N}.
$$

$$
RFC_s = \frac{FC_s}{N} = \frac{\sum_{i=i_1}^{^iN} UR_i}{N}
$$

$$
CV_{e} = {Uc_{e}}  \cdot{IC_{e}}  \cdot \sum {IUc_{e}}
$$

$$
p(M_\gamma | y, X) \; = \; \frac{p(y |M_\gamma, X) p(M_\gamma)}{p(y|X)} \;  = \frac{p(y |M_\gamma, X) p(M_\gamma)        }{\sum_{s=1}^{2^K} p(y| M_s, X) p(M_s)}
$$

$$ p(M_\gamma) = \theta^{k_\gamma} (1-\theta)^{K-k_\gamma} $$
Since expected model size is $\bar{m}= K \theta$, the researcher's prior choice reduces to eliciting a prior expected model size $\bar{m}$ (which defines $\theta$ via the relation $\theta=\bar{m}/K$). Choosing a prior model size of $K/2$ yields $\theta=\frac{1}{2}$ and thus exactly the uniform model prior $p(M_\gamma)=2^{-K}$. Therefore, putting prior model size at a value $<\frac{1}{2}$ tilts the prior distribution toward smaller model sizes and vice versa.

Let $y_{i}$ be a $(1 \times T)$ matrix containing a single endogenous variable from $Y$ for $i = 1, 2, ..., n$. Let $x_{i}$ be an $((L+1) \times T)$ matrix of $L$ lags of $y_{i}$ and a constant for $i = 1, 2, ..., n$. $\phi_{i}$ is a $(1 \times (L+1))$ matrix containing the lagged coefficients from the reduced form univariate Autoregression (AR) model for $i = 1, 2, ..., n$. $e_{i}$ is a $(1 \times T)$ matrix of the residuals from the univariate AR model for $i = 1, 2, ..., n$. $e$ is an $(n \times T)$ matrix of residuals from the univariate AR models. $\Sigma$ is an $(n \times n)$ symmetric covariance matrix of the residuals from the univariate AR models. $\Sigma_{i}$ is the $(i,i)$ element of $\Sigma$ for $i = 1, 2, ..., n$.

$p(A|Y)$ is the posterior density of $A|Y$. The products of $p(det(A))$ and/or $p(H)$ are multiplied by $p(A|Y)$ when priors are chosen for $det(A)$ and/or $H$ ($A^{-1}$), respectively. $p(A)$, $p(det(A))$, and $p(H)$ are products of the prior densities for $A$, $det(A)$, and $H$ ($A^{-1}$), respectively. $det(A)$ and $det(A \Omega A^{\top})$ are the determinants of the matrices $A$ and $A \Omega A^{\top}$, respectively.

$$
{\bfQ_t} = \left( {\bar \bfQ - \bfA'\bar Q\bfA - \bfB'\bar \bfQ\bfB - \bfG'{{\bar \bfQ}^ - }\bfG} \right) + \bfA'{\bfz_{t - 1}}{{\bfz'}_{t - 1}}\bfA + \bfB'{\bfQ_{t - 1}}\bfB + \bfG'\bfz_t^ - {{\bfz'}_t}^ - \bfG
$$

$$
{Q_{t + n}} = \left( {1 - \alpha  - \beta } \right)\bar Q + \alpha {E_t}\left[ {{z_{t + n - 1}}{{z'}_{t + n - 1}}} \right] + \beta {Q_{t + n - 1}}
$$

$$
{E_t}\left[ {{R_{t + n}}} \right] = \sum\limits_{i = 0}^{n - 2} {\left( {1 - \alpha  - \beta } \right)\bar R{{\left( {\alpha  + \beta } \right)}^i} + {{\left( {\alpha  + \beta } \right)}^{n - 1}}{R_{n + 1}}}
$$