What is Hidden Markov model, regime-switching model, Viterbi algorithm?

A hidden Markov model (HMM) has an unobserved state that follows a Markov chain (Book 4, chapter 8) and observations whose distribution depends on the current state; it is fitted by expectation-maximisation (Book 4, chapter 19), the Baum–Welch algorithm (Rabiner, 1989). A regime-switching model is an HMM for economic series, each state a regime with its own mean, volatility or dynamics (Hamilton, 1989; Ang and Timmermann, 2012). The Viterbi algorithm finds the single most likely path of states given all the observations, by dynamic programming.