Bayesian model rstan using comiler

$$\alpha\beta\gamma\epsilon\varepsilon\chi\varphi\phi\upsilon\varsigma\tau\rho\varpi\pio\xi\mu\lambda$$

$$
{\varepsilon _t} = H_t^{1/2}{z_t},
$$

$$
{H_t} = {D_t}R{D_t} = {\rho _{ij}}\sqrt {{h_{iit}}{h_{jjt}}},
$$

$$\Delta y_t = \Pi y_{t - 1} + \sum_{l = 1}^{p - 1} \Gamma_l \Delta y_{t - l} + C d_t + u_t,$$

f function `summary` is applied to an object of class `bvarlist`, it produces a table of information criteria for each specification. The information criteria are calculated based on the posterior draws of the respective model and calculated in the following way:

* *Log-likelihood*: $LL = \frac{1}{R} \sum_{i = 1}^{R} \left( \sum_{t = 1}^{T} -\frac{K}{2} \ln 2\pi - \frac{1}{2} \ln |\Sigma_t^{(i)}| -\frac{1}{2} (u_t^{{(i)}\prime} (\Sigma_t^{(i)})^{-1} u_t^{(i)} \right)$ for each draw $i$ and $u_t = y_t - \mu_t$;
* *Akaika information criterion*: $AIC = 2 (Kp + M (s + 1) + N) - 2 LL$;
* *Bayesian information criterion*: $BIC =  ln(T) (Kp + M (s + 1) + N) - 2 LL$;
* *Hannan-Quinn information criterion*: $HQ = 2 ln(ln(T)) (Kp + M (s + 1) + N) - 2 LL$.

$K$ is the number of endogenous variables and $p$ the lag order of the model. If exogenous variables were used $M$ is the number of stochastic exogenous regressors and $s$ is the lag order for those variables. $N$ is the number of deterministic terms.