$$ E[X_{t,i+1} \mid X_{t,1:i}] = E[\beta M_t] + E[\mu] + E[\nu_t] $$

$$ E[\beta M_t] = E[\beta] E[M_t] + E[(\beta - E[\beta])(M_t - E[M_t])] $$

$$ \begin{align*} X_t &= \beta M_t + \nu_t \ M_t &= \Phi M_{t-1} + \epsilon_t \end{align*} $$

$$ \mu \sim N(0, 0.1 I) $$