content_image/305635.jpg content_image/305640.jpg
Taking the first, second and third derivative of equation (A.30) and evaluating at t = 0 we get, 

<img src='content_image/305635.jpg'>

where m$_{1}$ ( Y ) , m$_{2}$ ( Y ) and m$_{3}$ ( Y ) are the first, second and third order central moments, respectively. Hence, skewness can be obtained as m 3 ( m 3 / 2 2 $_{)}$. ■ 

## Appendix B. Conditional Densities in FBQROR model 

In this appendix, we derive the conditional posteriors of the FBQROR model parameters. Specifically, the conditional posteriors of β, ν, h , and z have tractable distributions and is sampled using a Gibbs approach. The paraemters ( σ, γ ) are jointly sampled using random- walk MH algorithm (to reduce autocorrelation in MCMC draws) and δ is sampled using a random-walk MH algorithm. The derivations below follow the ordering as presented in Algorithm 1. 

(1) Starting with β , the conditional posterior π ( β | z, ν, h, σ, γ ) is proportional to π ( β ) × f ( z | β, ν, h, σ, γ ) and its kernel can be written as, 

<img src='content_image/305640.jpg'>

