Appendix to “ Bayesian Mixtures of Autoregressive Models ” published in the Journal of Computational and Graphical Statistics

j=1 |X ′ pZjXp + c−1X ′ pXp|b −aj j , where Zj = diag(ztjpr, t = P + 1, . . . , n). Note that ztjpr takes on the same value (zero or one) for all t ∈ {1 + (s − 1)L, . . . , sL}. The expressions for aj and bj are aj = 1 2 ∑n t=P+1 zjtpr + α and bj = 1 2 yMjy ∗ + β, where Mj = Zj − ZjXp(X ′ pZjXp + c−1X ′ pXp) −1X ′ pZj. 3. Let psjpr = sL ∏ t=1+(s−1)L p(yt|xt−1;φjpr, σ jpr). Draw the indicators from p(zsjpr = 1|yt, xt−1;φpr, δpr, σpr) = πsjpr psjpr ∑r h=1 πshpr psjpr , j = 1, . . . , r, t ∈ {1 + (s− 1)L, . . . , sL}, s = 1, . . . , S, where xt−1 = (yt−1, . . . , yt−p). 4. Draw δpr from p(δpr|zpr) = S ∏