Hidden Markov Models, Markov Chains, Markov Switching, Markov Auto Regression, Maximum Likelihood.
x_2t,…,x_mt] at time t, and β_cap_j is the vector of regime specific coefficients [β_cap_0j, β_cap_1j, β_cap_2j,…,β_cap_mj]. As we have seen in the 2-state Markov case (refer to Eq. 1), this yields a normally distributed probability density for y_t as follows: Probability density function