Markets seem to switch between calm and stormy periods, but nobody announces the switch. A hidden Markov model gives that idea a precise form: a hidden state moves by simple probabilities and each day's return is a noisy signal of it. This skill explains the model in plain steps, with short checks (numbers you compute, steps you order, concepts you match) and finance examples: how a chain of calm and stormy days behaves in the long run, how to update your belief about today's state from today's return, how to find the most likely path of states, how the model learns its own numbers from data, how many regimes are enough, and why a regime signal that looks at the whole history is a cheat. The capstone is a code lab where you write the algorithms yourself and detect regimes in real SPY returns.
Probability and basic Bayesian updating are expected (conditional probability, Bayes' rule). No Markov or HMM background is needed.
